<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">% -*- coding: utf-8 -*-
% This is part of the book TeX for the Impatient.
% Copyright (C) 2003 Paul W. Abrahams, Kathryn A. Hargreaves, Karl Berry.
% See file fdl.tex for copying conditions.

\input macros
%\chapter {Commands \linebreak for composing \linebreak math formulas}
\chapter {æ•°å­¦å…¬å¼å‘½ä»¤}

%\bix^^{math}
%\chapterdef{math}
\bix^^{æ•°å­¦}
\chapterdef{math}

%This section covers commands for constructing math formulas.
%For an explanation of the conventions used in this section,
%see \headcit{Descriptions of the commands}{cmddesc}.
è¿™ä¸€ç«&nbsp;åŒ…æ‹¬äº†æŽ’å°æ•°å­¦å…¬å¼æ‰€éœ€è¦çš„å‘½ä»¤ã€‚
åœ¨\headcit{å‘½ä»¤æè¿°}{cmddesc}è¿™ä¸€èŠ‚ä¸­ç»™å‡ºäº†è¿™ç«&nbsp;çš„æƒ¯ä¾‹ã€‚

\begindescriptions
%==========================================================================
%\section {Simple parts of formulas}
\section {ç®€å•å…¬å¼æŽ’ç‰ˆ}

%==========================================================================
%\subsection {Greek letters}
\subsection {å¸Œè…Šå­—æ¯}

%\begindesc
%\bix^^{Greek letters}
%\dothreecolumns 40
%\easy\ctsdisplay alpha {}
%\ctsdisplay beta {}
%\ctsdisplay chi {}
%\ctsdisplay delta {}
%\ctsdisplay Delta {}
%\ctsdisplay epsilon {}
%\ctsdisplay varepsilon {}
%\ctsdisplay eta {}
%\ctsdisplay gamma {}
%\ctsdisplay Gamma {}
%\ctsdisplay iota {}
%\ctsdisplay kappa {}
%\ctsdisplay lambda {}
%\ctsdisplay Lambda {}
%\ctsdisplay mu {}
%\ctsdisplay nu {}
%\ctsdisplay omega {}
%\ctsdisplay Omega {}
%\ctsdisplay phi {}
%\ctsdisplay varphi {}
%\ctsdisplay Phi {}
%\ctsdisplay pi {}
%\ctsdisplay varpi {}
%\ctsdisplay Pi {}
%\ctsdisplay psi {}
%\ctsdisplay Psi {}
%\ctsdisplay rho {}
%\ctsdisplay varrho {}
%\ctsdisplay sigma {}
%\ctsdisplay varsigma {}
%\ctsdisplay Sigma {}
%\ctsdisplay tau {}
%\ctsdisplay theta {}
%\ctsdisplay vartheta {}
%\ctsdisplay Theta {}
%\ctsdisplay upsilon {}
%\ctsdisplay Upsilon {}
%\ctsdisplay xi {}
%\ctsdisplay Xi {}
%\ctsdisplay zeta {}
%\egroup
\begindesc
\bix^^{å¸Œè…Šå­—æ¯}
\dothreecolumns 40
\easy\ctsdisplay alpha {}
\ctsdisplay beta {}
\ctsdisplay chi {}
\ctsdisplay delta {}
\ctsdisplay Delta {}
\ctsdisplay epsilon {}
\ctsdisplay varepsilon {}
\ctsdisplay eta {}
\ctsdisplay gamma {}
\ctsdisplay Gamma {}
\ctsdisplay iota {}
\ctsdisplay kappa {}
\ctsdisplay lambda {}
\ctsdisplay Lambda {}
\ctsdisplay mu {}
\ctsdisplay nu {}
\ctsdisplay omega {}
\ctsdisplay Omega {}
\ctsdisplay phi {}
\ctsdisplay varphi {}
\ctsdisplay Phi {}
\ctsdisplay pi {}
\ctsdisplay varpi {}
\ctsdisplay Pi {}
\ctsdisplay psi {}
\ctsdisplay Psi {}
\ctsdisplay rho {}
\ctsdisplay varrho {}
\ctsdisplay sigma {}
\ctsdisplay varsigma {}
\ctsdisplay Sigma {}
\ctsdisplay tau {}
\ctsdisplay theta {}
\ctsdisplay vartheta {}
\ctsdisplay Theta {}
\ctsdisplay upsilon {}
\ctsdisplay Upsilon {}
\ctsdisplay xi {}
\ctsdisplay Xi {}
\ctsdisplay zeta {}
\egroup
%\explain
%These commands produce Greek letters suitable for mathematics.
%You can only use them
%within a math formula, so if you need a Greek letter within ordinary
%text you must enclose it in dollar signs (|$|).  \TeX\ does not have
%commands for Greek letters that look like their roman
%counterparts, since you can get them by using those roman
%counterparts.  For example, you can get a lowercase
%^{omicron} in a formula by writing the letter `o', i.e.,
%`|{\rm o}|' or an uppercase ^{beta} (`B') by writing
%`|{\rm B}|'.
\explain
è¾“å…¥è¿™äº›å‘½ä»¤å¯ä»¥æŽ’å°å‡ºæ•°å­¦å…¬å¼ä¸­çš„ç›¸åº”çš„å¸Œè…Šå­—æ¯ç¬¦å·.
ä½&nbsp;åªèƒ½åœ¨æ•°å­¦æ¨¡å¼ä¸­ä½¿ç”¨å®ƒä»¬, æ‰€ä»¥å¦‚åœ¨æ™®é€šçš„æ–‡æœ¬ä¸­ä½¿ç”¨å®ƒä»¬æ—¶,
ä½&nbsp;å¿…é¡»æŠŠå®ƒä»¬æ‹¬åœ¨ç¾Žå…ƒç¬¦å· (|$|) å†….
\TeX\ å¹¶ä¸åŒ…å«è¿™äº›æ•°å­¦ä¸­ä½¿ç”¨çš„å¸Œè…Šå­—æ¯æ‰€å¯¹åº”çš„æ­£ä½“å­—ç¬¦çš„å‘½ä»¤,
ä¸è¿‡ä½&nbsp;å¯ä»¥å¾ˆæ–¹ä¾¿åœ°å¾—åˆ°è¿™äº›å­—ç¬¦.
æ¯”å¦‚è¯´, ä½&nbsp;å¯ä»¥åœ¨å…¬å¼ä¸­ä½¿ç”¨ `|{\rm o}|' æ¥å¾—åˆ°ä¸€ä¸ªå°å†™çš„ ^{omicron} `o',
åˆæ¯”å¦‚, ä½&nbsp;å¯ä»¥ä½¿ç”¨ `|{\rm B}|' å¾—åˆ°å¤§å†™çš„ ^{beta} (`B').

%Don't confuse the following letters:
%\ulist \compact
%\li |\upsilon| (`$\upsilon$'), |{\rm v}| (`v'), and |\nu| (`$\nu$').
%\li |\varsigma| (`$\varsigma$') and |\zeta| (`$\zeta$').
%\endulist
æ³¨æ„ä¸è¦æ··æ·†ä¸‹é¢çš„ç¬¦å·:
\ulist \compact
\li |\upsilon| (`$\upsilon$'), |{\rm v}| (`v'), å’Œ |\nu| (`$\nu$').
\li |\varsigma| (`$\varsigma$') å’Œ |\zeta| (`$\zeta$').
\endulist

%You can get slanted capital Greek letters by using the math italic
%(|\mit|) \minref{font}.
ä½¿ç”¨æ•°å­¦çš„æ„å¤§åˆ©\minref{å­—ä½“} (|\mit|) å¯ä»¥å¾—åˆ°æ–œä½“çš„å¤§å†™å¸Œè…Šå­—æ¯.

%\TeX\ treats Greek letters as ordinary symbols when it's figuring how
%much space to put around them.
åœ¨è®¡ç®—åœ¨å¸Œè…Šå­—æ¯å‘¨å›´æ’å…¥å¤šå°‘çš„ç©ºç™½æ—¶ï¼Œ\TeX\ æŠŠå®ƒä»¬å½“ä½œæ­£å¸¸çš„ç¬¦å·ã€‚

%\example
%If $\rho$ and $\theta$ are both positive, then $f(\theta)
%-{\mit \Gamma}_{\theta} &lt; f(\rho)-{\mit \Gamma}_{\rho}$.
%|
%\produces
%If $\rho$ and $\theta$ are both positive, then
%$f(\theta)-{\mit \Gamma}_{\theta} &lt; f(\rho)-{\mit \Gamma}_{\rho}$.
%\endexample
%\eix^^{Greek letters}
%\enddesc
\example
å¦‚æžœ $\rho$ å’Œ $\theta$ éƒ½æ˜¯æ­£æ•°, é‚£ä¹ˆ $f(\theta)
-{\mit \Gamma}_{\theta} &lt; f(\rho)-{\mit \Gamma}_{\rho}$.
|
\produces
å¦‚æžœ $\rho$ å’Œ $\theta$ éƒ½æ˜¯æ­£æ•°, é‚£ä¹ˆ
$f(\theta)-{\mit \Gamma}_{\theta} &lt; f(\rho)-{\mit \Gamma}_{\rho}$.
\endexample
\eix^^{å¸Œè…Šå­—æ¯}
\enddesc

%==========================================================================
%\subsection {Miscellaneous ordinary math symbols}
\subsection {å„ç§æ™®é€šæ•°å­¦ç¬¦å·}

\begindesc
\xrdef{specsyms}
\dothreecolumns 34
\easy\ctsdisplay infty {}
\ctsdisplay Re {}
\ctsdisplay Im {}
\ctsdisplay angle {}
\ctsdisplay triangle {}
\ctsdisplay backslash {}
\ctsdisplay vert {}
\writeidxfalse\ctsydisplay | @bar {}\writeidxtrue
\ctsdisplay Vert {}
\ctsdisplay emptyset {}
\ctsdisplay bot {}
\ctsdisplay top {}
\ctsdisplay exists {}
\ctsdisplay forall {}
\ctsdisplay hbar {}
\ctsdisplay ell {}
\ctsdisplay aleph {}
\ctsdisplay imath {}
\ctsdisplay jmath {}
\ctsdisplay nabla {}
\ctsdisplay neg {}
\ctsdisplay lnot {}
\actdisplay ' @prime \ (ä¸Šæ&nbsp;‡ç‚¹)
\ctsdisplay prime {}
\ctsdisplay partial {}
\ctsdisplay surd {}
\ctsdisplay wp {}
\ctsdisplay flat {}
\ctsdisplay sharp {}
\ctsdisplay natural {}
\ctsdisplay clubsuit {}
\ctsdisplay diamondsuit {}
\ctsdisplay heartsuit {}
\ctsdisplay spadesuit {}
\egroup
\explain
^^{éŸ³ç¬¦} ^^{èŠ±è‰²}
è¿™äº›å‘½ä»¤å¯ä»¥æŽ’å°å„ç§ç¬¦å·.
ä¸ºäº†æŠŠå®ƒä»¬å’Œå…¶å®ƒçš„ç¬¦å·, æ¯”å¦‚å…³ç³»ç¬¦å·ç­‰, åŒºåˆ†å¼€æ¥, å®ƒä»¬è¢«ç§°ä¸ºæ™®é€šæ•°å­¦ç¬¦å·.
ä½&nbsp;åªèƒ½åœ¨æ•°å­¦æ¨¡å¼ä¸­ä½¿ç”¨è¿™äº›ç¬¦å·, æ‰€ä»¥å¦‚æžœåœ¨æ™®é€šçš„æ–‡æœ¬ä¸­ä½¿ç”¨, ä½&nbsp;å¿…é¡»ä½¿ç”¨ç¾Žå…ƒç¬¦å· (|$|) æŠŠå®ƒä»¬æ‹¬èµ·æ¥.

å½“ä½&nbsp;æƒ³åœ¨ `$i$' æˆ– `$j$' ä¸ŠåŠ&nbsp;ä¸Šé‡éŸ³ç¬¦å·, åˆ™éœ€è¦ä½¿ç”¨ |\imath| å’Œ |\jmath| å‘½ä»¤æ¥è¡¨ç¤ºå®ƒä»¬æœ¬èº«.

ä¸Šæ&nbsp;‡ç‚¹ç¬¦å· (|'|) æ˜¯ä¸€ä¸ª |\prime| çš„ä¸Šæ&nbsp;‡çš„ç®€å†™.
(|\prime| æœ¬èº«å¯ä»¥æŽ’å°ä¸€ä¸ªå¾ˆå¤§çš„ä¸‘é™‹çš„æ’‡å·.)

|\!|| å’Œ ^|\Vert| å‘½ä»¤æ˜¯ç­‰ä»·çš„, å°±åƒ ^|\neg| å’Œ ^|\lnot| å‘½ä»¤ä¸€æ&nbsp;·.
\margin{å¢žåŠ&nbsp;äº† {\tt\\vert} çš„è§£é‡Š}
|\vert| ç¬¦å·å¯ä»¥æŽ’å°å‡ºå’Œ `|!||' ç›¸åŒçš„æ•ˆæžœ.
\indexchar |

ç”± |\backslash|, |\vert|, å’Œ |\Vert| æŽ’å°çš„å‘½ä»¤å«åš \minref{åˆ†ç•Œç¬¦}.
ä½¿ç”¨ ^|\bigm| ç­‰ (\xref \bigm) å‘½ä»¤å¯ä»¥æŽ’å°å¤§å·çš„è¿™äº›å­—ç¬¦.

\example
The Knave of $\heartsuit$s, he stole some tarts.
|
\produces
The Knave of $\heartsuit$s, he stole some tarts.
\nextexample
å¦‚ $\hat\imath &lt; \hat\jmath$ åˆ™ $i' \leq j^\prime$.
|
\produces
å¦‚ $\hat\imath &lt; \hat\jmath$ åˆ™ $i' \leq j^\prime$.
\nextexample
$${{x-a}\over{x+a}}\biggm\backslash{{y-b}\over{y+b}}$$
|
\dproduces
$${{x-a}\over{x+a}}\biggm\backslash{{y-b}\over{y+b}}$$
\endexample
\enddesc

%==========================================================================
\subsection {äºŒå…ƒè¿ç®—ç¬¦}

\begindesc
\bix^^{è¿ç®—ç¬¦}
\xrdef{binops}
\dothreecolumns 34
\easy\ctsdisplay vee {}
\ctsdisplay wedge {}
\ctsdisplay amalg {}
\ctsdisplay cap {}
\ctsdisplay cup {}
\ctsdisplay uplus {}
\ctsdisplay sqcap {}
\ctsdisplay sqcup {}
\ctsdisplay dagger {}
\ctsdisplay ddagger {}
\ctsdisplay land {}
\ctsdisplay lor {}
\ctsdisplay cdot {}
\ctsdisplay diamond {}
\ctsdisplay bullet {}
\ctsdisplay circ {}
\ctsdisplay bigcirc {}
\ctsdisplay odot {}
\ctsdisplay ominus {}
\ctsdisplay oplus {}
\ctsdisplay oslash {}
\ctsdisplay otimes {}
\ctsdisplay pm {}
\ctsdisplay mp {}
\ctsdisplay triangleleft {}
\ctsdisplay triangleright {}
\ctsdisplay bigtriangledown {}
\ctsdisplay bigtriangleup {}
\ctsdisplay ast {}
\ctsdisplay star {}
\ctsdisplay times {}
\ctsdisplay div {}
\ctsdisplay setminus {}
\ctsdisplay wr {}
\egroup
\explain
è¿™äº›å‘½ä»¤å¯ä»¥æŽ’å°å„ç§äºŒå…ƒè¿ç®—ç¬¦.
äºŒå…ƒè¿ç®—ç¬¦æ˜¯ \TeX\ çš„ä¸€ç§ç¬¦å·\minref{é›†}.
\TeX\ åœ¨ä¸åŒçš„ç¬¦å·é›†å‘¨å›´ä¼šæ’å…¥ä¸åŒçš„ç©ºç™½.
å½“ \TeX\ éœ€è¦åœ¨ä¸€ä¸ªæ•°å­¦å…¬å¼ä¸­é—´æ–­è¡Œæ—¶,
å®ƒä¼šè€ƒè™‘åœ¨äºŒå…ƒè¿ç®—ç¬¦åŽé¢è¿›è¡Œæ–­è¡Œ---ä¸è¿‡ä»…åœ¨å®ƒå‡ºçŽ°åœ¨å…¬å¼çš„æœ€å¤–å±‚æ—¶, è€Œä¸æ˜¯åœ¨ä¸€ä¸ªç»„ä¸­.

é™¤äº†è¿™äº›å‘½ä»¤ä»¥å¤–, \TeX\ ä¹ŸæŠŠ `|+|' and `|-|' ä½œä¸ºäºŒå…ƒè¿ç®—ç¬¦.
å®ƒæŠŠ `|/|' å½“ä½œä¸€ä¸ªæ™®é€šç¬¦å·,
å›&nbsp;ä¸ºè™½ç„¶äº‹å®žä¸Šåœ¨æ•°å­¦ä¸­å®ƒæ˜¯ä¸€ä¸ªäºŒå…ƒè¿ç®—,
ä½†æ˜¯å®ƒåœ¨å‘¨å›´åŠ&nbsp;å…¥çš„ç©ºç™½æ›´å°‘æ—¶çœ‹ä¸ŠåŽ»æ›´æ¼‚äº®.

\example
$$z = x \div y \quad \hbox{å½“ä¸”ä»…å½“} \quad
z \times y = x \;\hbox{ä¸”}\; y \neq 0$$
|
\dproduces
$$z = x \div y \quad \hbox{å½“ä¸”ä»…å½“} \quad
z \times y = x \;\hbox{ä¸”}\; y \neq 0$$
\endexample
\enddesc

\begindesc
\ctspecial * \ctsxrdef{@star}
\explain
å‘½ä»¤ |\*| è¡¨ç¤ºä¹˜æ³•ç¬¦å· ($\times$), ä¹Ÿæ˜¯ä¸€ä¸ªäºŒå…ƒç¬¦å·.
ä¹˜æ³•ç¬¦å·åœ¨æ–‡æœ¬ä¸­çš„æ•°å­¦å…¬å¼ä¸­å‡ºçŽ°æ—¶è¡¨çŽ°å¾—å’Œä¸€ä¸ªåˆ†è¯ç¬¦ç±»ä¼¼.
è¿™å°±æ˜¯è¯´, \TeX\ \emph{ä»…}ä¼šåœ¨å…¬å¼è¯¥ç‚¹éœ€è¦æ–­è¡Œæ—¶æŽ’ç‰ˆ |\times| ç¬¦å·.
å›&nbsp;ä¸º \TeX\ æ°¸è¿œä¸ä¼šåœ¨é™ˆåˆ—å…¬å¼ä¸­æ–­è¡Œ, æ‰€ä»¥ |\*| åœ¨é™ˆåˆ—å…¬å¼ \minrefs{é™ˆåˆ—å…¬å¼} ä¸­æ˜¯æ²¡æœ‰ä»»ä½•ä½œç”¨çš„.

\example
Let $c = a\*b$. In the case that $c=0$ or $c=1$, let
$\Delta$ be $(\hbox{the smallest $q$})\*(\hbox{the
largest $q$})$ in the set of approximate $\tau$-values.
|
\produces
Let $c = a\*b$. In the case that $c=0$ or $c=1$, let
$\Delta$ be $(\hbox{the smallest $q$})\*(\hbox{the
largest $q$})$ in the set of approximate $\tau$-values.

\eix^^{è¿ç®—ç¬¦}
\endexample
\enddesc

%==========================================================================
\subsection {å…³ç³»ç¬¦å·}

\begindesc
\xrdef {relations}
\bix^^{å…³ç³»ç¬¦}
\dothreecolumns 39
\easy\ctsdisplay asymp {}
\ctsdisplay cong {}
\ctsdisplay dashv {}
\ctsdisplay vdash {}
\ctsdisplay perp {}
\ctsdisplay mid {}
\ctsdisplay parallel {}
\ctsdisplay doteq {}
\ctsdisplay equiv {}
\ctsdisplay ge {}
\ctsdisplay geq {}
\ctsdisplay le {}
\ctsdisplay leq {}
\ctsdisplay gg {}
\ctsdisplay ll {}
\ctsdisplay models {}
\ctsdisplay ne {}
\ctsdisplay neq {}
\ctsdisplay notin {}
\ctsdisplay in {}
\ctsdisplay ni {}
\ctsdisplay owns {}
\ctsdisplay prec {}
\ctsdisplay preceq {}
\ctsdisplay succ {}
\ctsdisplay succeq {}
\ctsdisplay bowtie {}
\ctsdisplay propto {}
\ctsdisplay approx {}
\ctsdisplay sim {}
\ctsdisplay simeq {}
\ctsdisplay frown {}
\ctsdisplay smile {}
\ctsdisplay subset {}
\ctsdisplay subseteq {}
\ctsdisplay supset {}
\ctsdisplay supseteq {}
\ctsdisplay sqsubseteq {}
\ctsdisplay sqsupseteq {}
\egroup
\explain
è¿™äº›å‘½ä»¤å¯ä»¥æŽ’å°å„ç§å…³ç³»ç¬¦å·.
å…³ç³»ç¬¦å·æ˜¯ \TeX\ çš„æ•°å­¦ç¬¦å·ä¸­çš„\minref{ç±»}ä¹‹ä¸€.
\TeX\ åœ¨ä¸åŒçš„\minref{ç±»}ä¹‹é—´æ’å…¥ä¸åŒçš„ç©ºç™½é•¿åº¦.
å½“ \TeX\ éœ€è¦åœ¨ä¸€ä¸ªæ•°å­¦å…¬å¼å¤„æ–­è¡Œ, \minrefs{æ–­è¡Œ}
å®ƒä¼šè€ƒè™‘åœ¨ä¸€ä¸ªå…³ç³»ç¬¦åŽè¿›è¡Œæ–­è¡Œ---ä¸è¿‡ä»…åœ¨å®ƒå‡ºçŽ°åœ¨å…¬å¼çš„æœ€å¤–å±‚æ—¶, è€Œä¸æ˜¯åœ¨ä¸€ä¸ªç»„ä¸­.

é™¤äº†è¿™é‡Œåˆ—å‡ºçš„å‘½ä»¤ä»¥å¤–, \TeX\ ä¹ŸæŠŠ `^|=|' å’Œ``arrow'' å‘½ä»¤ (\xref{arrows}) ä½œä¸ºå…³ç³»è¿ç®—ç¬¦.

ä¸€äº›å…³ç³»ç¬¦æœ‰å¤šç§å‘½ä»¤è¡¨è¾¾æ–¹å¼, ä½&nbsp;å¯ä»¥ä½¿ç”¨ä»»ä½•ä¸€ä¸ªæ¥æŽ’å°å®ƒä»¬:
\ulist \compact
\li `$\ge$' (|\ge| å’Œ |\geq|).
\li `$\le$' (|\le| å’Œ |\leq|).
\li `$\ne$' (|\ne|, |\neq|, å’Œ |\not=|).
\li `$\ni$' (|\ni| å’Œ |\owns|).
\endulist

\xrdef{\not}
åœ¨è¿™äº›ç¬¦å·å‰åŠ&nbsp;ä¸Š |\not|, å¯ä»¥æŽ’å°å®ƒä»¬çš„éžè¿ç®—:

\nobreak
\threecolumns 21
\basicdisplay {$\not\asymp$}{\\not\\asymp}\ctsidxref{asymp}
\basicdisplay {$\not\cong$}{\\not\\cong}\ctsidxref{cong}
\basicdisplay {$\not\equiv$}{\\not\\equiv}\ctsidxref{equiv}
\basicdisplay {$\not=$}{\\not=}\ttidxref{=}
\basicdisplay {$\not\ge$}{\\not\\ge}\ctsidxref{ge}
\basicdisplay {$\not\geq$}{\\not\\geq}\ctsidxref{geq}
\basicdisplay {$\not\le$}{\\not\\le}\ctsidxref{le}
\basicdisplay {$\not\leq$}{\\not\\leq}\ctsidxref{leq}
\basicdisplay {$\not\prec$}{\\not\\prec}\ctsidxref{prec}
\basicdisplay {$\not\preceq$}{\\not\\preceq}\ctsidxref{preceq}
\basicdisplay {$\not\succ$}{\\not\\succ}\ctsidxref{succ}
\basicdisplay {$\not\succeq$}{\\not\\succeq}\ctsidxref{succeq}
\basicdisplay {$\not\approx$}{\\not\\approx}\ctsidxref{approx}
\basicdisplay {$\not\sim$}{\\not\\sim}\ctsidxref{sim}
\basicdisplay {$\not\simeq$}{\\not\\simeq}\ctsidxref{simeq}
\basicdisplay {$\not\subset$}{\\not\\subset}\ctsidxref{subset}
\basicdisplay {$\not\subseteq$}{\\not\\subseteq}\ctsidxref{subseteq}
\basicdisplay {$\not\supset$}{\\not\\supset}\ctsidxref{supset}
\basicdisplay {$\not\supseteq$}{\\not\\supseteq}\ctsidxref{supseteq}
\basicdisplay {$\not\sqsubseteq$}{\\not\\sqsubseteq}%
   \ctsidxref{sqsubseteq}
\basicdisplay {$\not\sqsupseteq$}{\\not\\sqsupseteq}%
   \ctsidxref{sqsupseteq}
\egroup

\example
æˆ‘ä»¬å¯ä»¥å¾—åˆ° $AB \perp AC$,ä¸”
$\triangle ABF \not\sim \triangle ACF$.
|
\produces
æˆ‘ä»¬å¯ä»¥å¾—åˆ° $AB \perp AC$,ä¸”
$\triangle ABF \not\sim \triangle ACF$.

\eix^^{å…³ç³»ç¬¦}
\endexample
\enddesc

%==========================================================================
%\subsection {Left and right delimiters}
\subsection {å·¦å³å®šç•Œç¬¦}

%\begindesc
%\bix^^{delimiters}
%%
%\dothreecolumns 12
%\easy\ctsdisplay lbrace {}
%\ctsydisplay { @lbrace {}
%\ctsdisplay rbrace {}
%\ctsydisplay } @rbrace {}
%\ctsdisplay lbrack {}
%\ctsdisplay rbrack {}
%\ctsdisplay langle {}
%\ctsdisplay rangle {}
%\ctsdisplay lceil {}
%\ctsdisplay rceil {}
%\ctsdisplay lfloor {}
%\ctsdisplay rfloor {}
%\egroup
%\explain
%These commands produce left and right \minref{delimiter}s.
%Mathematicians use delimiters to indicate the boundaries between parts
%of a formula.  Left delimiters are also called ``^{opening}s'', and
%right delimiters are also called ``^{closing}s''.  Openings and closings
%are two of \TeX's \minref{class}es of math symbols.  \TeX\ puts
%different amounts of space around different \minref{class}es of math
%symbols. You might expect the space that \TeX\ puts around openings and
%closings to be symmetrical, but in fact it isn't.
\begindesc
\bix^^{å®šç•Œç¬¦}
%
\dothreecolumns 12
\easy\ctsdisplay lbrace {}
\writeidxfalse\ctsydisplay { @lbrace {}\writeidxtrue
\ctsdisplay rbrace {}
\writeidxfalse\ctsydisplay } @rbrace {}\writeidxtrue
\ctsdisplay lbrack {}
\ctsdisplay rbrack {}
\ctsdisplay langle {}
\ctsdisplay rangle {}
\ctsdisplay lceil {}
\ctsdisplay rceil {}
\ctsdisplay lfloor {}
\ctsdisplay rfloor {}
\egroup
\explain
è¿™äº›å‘½ä»¤æŽ’å°å„ç§å·¦å³\minref{å®šç•Œç¬¦}ã€‚
æ•°å­¦å®¶ç”¨å®šç•Œç¬¦æŒ‡æ˜Žå…¬å¼å„éƒ¨åˆ†çš„è¾¹ç•Œã€‚
å·¦å®šç•Œç¬¦åˆç§°ä¸º``^{å¼€ç¬¦å·}''ï¼Œå³å®šç•Œç¬¦åˆç§°ä¸º``^{é—­ç¬¦å·}''ã€‚
å¼€ç¬¦å·å’Œé—­ç¬¦å·æ˜¯ \TeX\ æ•°å­¦å…¬å¼ä¸­çš„ä¸¤ç§å­—ç¬¦ç±»ã€‚
\TeX\ åœ¨ä¸åŒ\minref{ç±»}çš„æ•°å­¦ç¬¦å·ä¹‹é—´ç•™ä¸‹ä¸åŒå¤§å°çš„é—´éš”ã€‚
ä½&nbsp;ä¹Ÿè®¸è®¤ä¸ºåœ¨å¼€ç¬¦å·å’Œé—­ç¬¦å·æ—è¾¹çš„é—´éš”æ˜¯å¯¹ç§°çš„ï¼Œä½†å®žé™…ä¸Šå¹¶éžå¦‚æ­¤ã€‚

%Some left and right delimiters have more than one command that you can
%use to produce them:
æœ‰äº›å·¦å®šç•Œç¬¦å’Œå³å®šç•Œç¬¦å¯ä»¥ç”¨ä¸æ­¢ä¸€ä¸ªå‘½ä»¤æŽ’å°ï¼š

%\ulist\compact
%\li `$\{$' (|\lbrace| and |\{|)
%\li `$\}$' (|\rbrace| and |\}|)
%\li `$[$' (|\lbrack| and `|[|')
%\li `$]$' (|\rbrack| and `|]|')
%\endulist
%\noindent You can also use the left and right bracket characters
%(in either form) outside of math mode.
\ulist\compact
\li `$\{$' (|\lbrace| å’Œ |\{|)
\li `$\}$' (|\rbrace| å’Œ |\}|)
\li `$[$' (|\lbrack| å’Œ `|[|')
\li `$]$' (|\rbrack| å’Œ `|]|')
\endulist
\noindent å·¦å³æ–¹æ‹¬å·ï¼ˆä¸¤ç§å½¢å¼çš†å¯ï¼‰åœ¨æ•°å­¦æ¨¡å¼ä¹‹å¤–ä¹Ÿå¯ä»¥ä½¿ç”¨ã€‚

%In addition to these commands, \TeX\ treats `|(|' as a left
%delimiter and `|)|' as a right delimiter.
é™¤è¿™äº›å‘½ä»¤ä¹‹å¤–ï¼Œ\TeX\ è¿˜å°† `|(|' è§†ä¸ºå·¦å®šç•Œç¬¦ï¼Œå°† `|)|' è§†ä¸ºå³å®šç•Œç¬¦ã€‚

%You can have \TeX\
%choose the size for a delimiter by using |\left| and |\right| (\xref\left).
%Alternatively,
%you can get a delimiter of a specific size by using one of the |\big|$x$
%commands (see |\big| et al., \xref{\big}).
åˆ©ç”¨ |\left| å’Œ |\right|ï¼ˆ\xref\left ï¼‰å‘½ä»¤ï¼Œ
ä½&nbsp;å¯ä»¥è®© \TeX\ é€‰æ‹©å®šç•Œç¬¦çš„å°ºå¯¸ã€‚
æˆ–è€…åˆ©ç”¨æŸä¸ª |\big|$x$ å‘½ä»¤ï¼ˆè§ |\big| ç­‰ï¼Œ\xref{\big}ï¼‰ï¼Œ
ä½&nbsp;å¯ä»¥é€‰æ‹©ç‰¹å®šå°ºå¯¸çš„å®šç•Œç¬¦ã€‚

%\example
%The set $\{\,x \mid x&gt;0\,\}$ is empty.
%|
%\produces
%The set $\{\,x \mid x&gt;0\,\}$ is empty.
\example
é›†åˆ $\{\,x \mid x&gt;0\,\}$ æ˜¯ç©ºé›†.
|
\produces
é›†åˆ $\{\,x \mid x&gt;0\,\}$ æ˜¯ç©ºé›†.

%\eix^^{delimiters}
%\endexample
%\enddesc
\eix^^{å®šç•Œç¬¦}
\endexample
\enddesc

%==========================================================================
%\subsection {Arrows}
\subsection {ç®­å¤´}

%\begindesc
%\bix^^{arrows}
%\xrdef{arrows}
%%
%{\symbolspace=24pt \makecolumns 34/2:
%\easy%
%\ctsdisplay leftarrow {}
%\ctsdisplay gets {}
%\ctsdisplay Leftarrow {}
%\ctsdisplay rightarrow {}
%\ctsdisplay to {}
%\ctsdisplay Rightarrow {}
%\ctsdisplay leftrightarrow {}
%\ctsdisplay Leftrightarrow {}
%\ctsdisplay longleftarrow {}
%\ctsdisplay Longleftarrow {}
%\ctsdisplay longrightarrow {}
%\ctsdisplay Longrightarrow {}
%\ctsdisplay longleftrightarrow {}
%\ctsdisplay Longleftrightarrow {}
%\basicdisplay {$\Longleftrightarrow$}{\\iff}\pix\ctsidxref{iff}\xrdef{\iff}
%\ctsdisplay hookleftarrow {}
%\ctsdisplay hookrightarrow {}
%\ctsdisplay leftharpoondown {}
%\ctsdisplay rightharpoondown {}
%\ctsdisplay leftharpoonup {}
%\ctsdisplay rightharpoonup {}
%\ctsdisplay rightleftharpoons {}
%\ctsdisplay mapsto {}
%\ctsdisplay longmapsto {}
%\ctsdisplay downarrow {}
%\ctsdisplay Downarrow {}
%\ctsdisplay uparrow {}
%\ctsdisplay Uparrow {}
%\ctsdisplay updownarrow {}
%\ctsdisplay Updownarrow {}
%\ctsdisplay nearrow {}
%\ctsdisplay searrow {}
%\ctsdisplay nwarrow {}
%\ctsdisplay swarrow {}
%}
%\explain
%These commands provide arrows of different kinds.  They
%are classified as relations (\xref{relations}).
%The vertical arrows in the list are also \minref{delimiter}s, so you can make
%them larger by using |\big| et al.\ (\xref \big).
\begindesc
\bix^^{ç®­å¤´}
\xrdef{arrows}
%
{\symbolspace=24pt \makecolumns 34/2:
\easy%
\ctsdisplay leftarrow {}
\ctsdisplay gets {}
\ctsdisplay Leftarrow {}
\ctsdisplay rightarrow {}
\ctsdisplay to {}
\ctsdisplay Rightarrow {}
\ctsdisplay leftrightarrow {}
\ctsdisplay Leftrightarrow {}
\ctsdisplay longleftarrow {}
\ctsdisplay Longleftarrow {}
\ctsdisplay longrightarrow {}
\ctsdisplay Longrightarrow {}
\ctsdisplay longleftrightarrow {}
\ctsdisplay Longleftrightarrow {}
\basicdisplay {$\Longleftrightarrow$}{\\iff}\pix\ctsidxref{iff}\xrdef{\iff}
\ctsdisplay hookleftarrow {}
\ctsdisplay hookrightarrow {}
\ctsdisplay leftharpoondown {}
\ctsdisplay rightharpoondown {}
\ctsdisplay leftharpoonup {}
\ctsdisplay rightharpoonup {}
\ctsdisplay rightleftharpoons {}
\ctsdisplay mapsto {}
\ctsdisplay longmapsto {}
\ctsdisplay downarrow {}
\ctsdisplay Downarrow {}
\ctsdisplay uparrow {}
\ctsdisplay Uparrow {}
\ctsdisplay updownarrow {}
\ctsdisplay Updownarrow {}
\ctsdisplay nearrow {}
\ctsdisplay searrow {}
\ctsdisplay nwarrow {}
\ctsdisplay swarrow {}
}
\explain
è¿™äº›å‘½ä»¤æä¾›å„ç§ç®­å¤´ã€‚å®ƒä»¬è¢«åˆ’åˆ†ä¸ºå…³ç³»ç¬¦å·ï¼ˆ\xref{relations}ï¼‰ã€‚
ä¸Šé¢çš„ç«–ç›´ç®­å¤´åŒæ—¶ä¹Ÿæ˜¯\minref{å®šç•Œç¬¦}ï¼Œ
å›&nbsp;æ­¤ä½&nbsp;å¯ä»¥ç”¨ |\big| ç­‰å‘½ä»¤è®©å®ƒä»¬å˜å¤§ï¼ˆ\xref \big ï¼‰ã€‚

%The command |\iff| differs from |\Longleftrightarrow| in that
%it produces extra space to the left and right of the arrow.
å‘½ä»¤ |\iff| å’Œ |\Longleftrightarrow| çš„å·®åˆ«ä¹‹å¤„åœ¨äºŽï¼Œ
å®ƒåœ¨ç®­å¤´ä¸¤è¾¹ç”Ÿæˆé¢å¤–é—´éš”ã€‚

%You can place symbols or other legends on top of a left or right arrow
%with |\buildrel| (\xref \buildrel).
ä½&nbsp;å¯ä»¥ç”¨ |\buildrel|ï¼ˆ\xref \buildrel ï¼‰å‘½ä»¤å°†ç¬¦å·æˆ–è€…å…¶ä»–æ–‡å­—æ”¾åœ¨ç®­å¤´ä¸Šè¾¹ã€‚

%\example
%$$f(x)\mapsto f(y) \iff x \mapsto y$$
%|
%\dproduces
%$$f(x)\mapsto f(y) \iff x \mapsto y$$
\example
$$f(x)\mapsto f(y) \iff x \mapsto y$$
|
\dproduces
$$f(x)\mapsto f(y) \iff x \mapsto y$$

%\eix^^{arrows}
%\endexample
%\enddesc
\eix^^{ç®­å¤´}
\endexample
\enddesc

%==========================================================================
%\subsection {Named mathematical functions}
\subsection {å·²å‘½åçš„æ•°å­¦å‡½æ•°}

%\begindesc
%\xrdef{namedfns}
%\bix^^{functions, names of}
%{\symbolspace = 36pt
%\threecolumns 32
%\easy\ctsdisplay cos {}
%\ctsdisplay sin {}
%\ctsdisplay tan {}
%\ctsdisplay cot {}
%\ctsdisplay csc {}
%\ctsdisplay sec {}
%\ctsdisplay arccos {}
%\ctsdisplay arcsin {}
%\ctsdisplay arctan {}
%\ctsdisplay cosh {}
%\ctsdisplay coth {}
%\ctsdisplay sinh {}
%\ctsdisplay tanh {}
%\ctsdisplay det {}
%\ctsdisplay dim {}
%\ctsdisplay exp {}
%\ctsdisplay ln {}
%\ctsdisplay log {}
%\ctsdisplay lg {}
%\ctsdisplay arg {}
%\ctsdisplay deg {}
%\ctsdisplay gcd {}
%\ctsdisplay hom {}
%\ctsdisplay ker {}
%\ctsdisplay inf {}
%\ctsdisplay sup {}
%\ctsdisplay lim {}
%\ctsdisplay liminf {}
%\ctsdisplay limsup {}
%\ctsdisplay max {}
%\ctsdisplay min {}
%\ctsdisplay Pr {}
%\egroup}
%\explain
%These commands set the names of various mathematical functions
%in roman type, as is customary.
%If you apply a superscript or subscript to one of these commands,
%\TeX\ will in most cases typeset it in the usual place.
%In display style, \TeX\ typesets superscripts and subscripts
%on |\det|, |\gcd|, |\inf|, |\lim|, |\liminf|,
%|\limsup|, |\max|, |\min|, |\Pr|, and |\sup|
%as though they were limits,
%i.e., directly above or directly below the function name.
\begindesc
\xrdef{namedfns}
\bix^^{å‡½æ•°åç§°}
{\symbolspace = 36pt
\threecolumns 32
\easy\ctsdisplay cos {}
\ctsdisplay sin {}
\ctsdisplay tan {}
\ctsdisplay cot {}
\ctsdisplay csc {}
\ctsdisplay sec {}
\ctsdisplay arccos {}
\ctsdisplay arcsin {}
\ctsdisplay arctan {}
\ctsdisplay cosh {}
\ctsdisplay coth {}
\ctsdisplay sinh {}
\ctsdisplay tanh {}
\ctsdisplay det {}
\ctsdisplay dim {}
\ctsdisplay exp {}
\ctsdisplay ln {}
\ctsdisplay log {}
\ctsdisplay lg {}
\ctsdisplay arg {}
\ctsdisplay deg {}
\ctsdisplay gcd {}
\ctsdisplay hom {}
\ctsdisplay ker {}
\ctsdisplay inf {}
\ctsdisplay sup {}
\ctsdisplay lim {}
\ctsdisplay liminf {}
\ctsdisplay limsup {}
\ctsdisplay max {}
\ctsdisplay min {}
\ctsdisplay Pr {}
\egroup}
\explain
è¿™äº›å‘½ä»¤ä»¥æƒ¯ç”¨çš„ç½—é©¬å­—ä½“æŽ’å°å„ç§æ•°å­¦å‡½æ•°çš„åç§°ã€‚
å¦‚æžœä½&nbsp;ç»™è¿™äº›å‘½ä»¤ä¸­çš„ä»»ä½•ä¸€ä¸ªåŠ&nbsp;ä¸Šä¸Šæ&nbsp;‡æˆ–ä¸‹æ&nbsp;‡ï¼Œ
\TeX\ å°†åœ¨é€šå¸¸çš„ä½ç½®æŽ’ç‰ˆå®ƒã€‚
åœ¨é™ˆåˆ—æ&nbsp;·å¼ä¸­ï¼Œå¯¹äºŽ |\det|ã€|\gcd|ã€|\inf|ã€|\lim|ã€|\liminf|ã€
|\limsup|ã€|\max|ã€|\min|ã€|\Pr| å’Œ |\sup|ï¼Œ
\TeX\ å°†ä¸Šæ&nbsp;‡å’Œä¸‹æ&nbsp;‡å½“æˆæžé™é‚£æ&nbsp;·æŽ’ç‰ˆï¼Œ
å³å°†å®ƒä»¬ç›´æŽ¥æ”¾åœ¨å‡½æ•°åçš„ä¸Šè¾¹æˆ–ä¸‹è¾¹ã€‚

%\example
%$\cos^2 x + \sin^2 x = 1\qquad\max_{a \in A} g(a) = 1$
%|
%\produces
%$\cos^2 x + \sin^2 x = 1\qquad\max_{a \in A} g(a) = 1$
%\endexample\enddesc
\example
$\cos^2 x + \sin^2 x = 1\qquad\max_{a \in A} g(a) = 1$
|
\produces
$\cos^2 x + \sin^2 x = 1\qquad\max_{a \in A} g(a) = 1$
\endexample\enddesc

%\begindesc
%\cts bmod {}
%\explain
%This command produces a binary operation for indicating a ^{modulus}
%within a formula.
%\example
%$$x = (y+1) \bmod 2$$
%|
%\dproduces
%$$x = (y+1) \bmod 2$$
%\endexample
%\enddesc
\begindesc
\cts bmod {}
\explain
æ­¤å‘½ä»¤æŽ’å°ä¸€ä¸ªæ&nbsp;‡æ˜Žå…¬å¼å†…çš„^{æ¨¡è¿ç®—}çš„äºŒå…ƒè¿ç®—ç¬¦ã€‚
\example
$$x = (y+1) \bmod 2$$
|
\dproduces
$$x = (y+1) \bmod 2$$
\endexample
\enddesc

%\begindesc
%\cts pmod {}
%\explain
%This command provides a notation for indicating a ^{modulus} in parentheses
%at the end of a formula.
%\example
%$$x \equiv y+1 \pmod 2$$
%|
%\dproduces
%$$x \equiv y+1 \pmod 2$$
\begindesc
\cts pmod {}
\explain
æ­¤å‘½ä»¤åœ¨å…¬å¼æœ«å°¾æŽ’å°æ”¾åœ¨åœ†æ‹¬å·ä¸­çš„^{æ¨¡è¿ç®—}ã€‚
\example
$$x \equiv y+1 \pmod 2$$
|
\dproduces
$$x \equiv y+1 \pmod 2$$

%\eix^^{functions, names of}
%\endexample
%\enddesc
\eix^^{å‡½æ•°åç§°}
\endexample
\enddesc


%==========================================================================
%\subsection {Large operators}
\subsection {å·¨ç®—ç¬¦}

%\begindesc
%\bix^^{operators//large}
%\threecolumns 15
%\easy\ctsdoubledisplay bigcap {}
%\ctsdoubledisplay bigcup {}
%\ctsdoubledisplay bigodot {}
%\ctsdoubledisplay bigoplus {}
%\ctsdoubledisplay bigotimes {}
%\ctsdoubledisplay bigsqcup {}
%\ctsdoubledisplay biguplus {}
%\ctsdoubledisplay bigvee {}
%\ctsdoubledisplay bigwedge {}
%\ctsdoubledisplay coprod {}
%{\symbolspace = 42pt\basicdisplay {\hskip 26pt$\smallint$}%
%   {\\smallint}\ddstrut}%
%   \xrdef{\smallint} \pix\ctsidxref{smallint}
%\ctsdoubledisplay int {}
%\ctsdoubledisplay oint {}
%\ctsdoubledisplay prod {}
%\ctsdoubledisplay sum {}
%}
%\explain
%These commands produce various large operator symbols.
%\TeX\ produces the smaller size when it's in ^{text style}
%\minrefs{math mode} and the larger size when it's in ^{display style}.
%Operators are one of \TeX's \minref{class}es of math symbols.
%\TeX\ puts different amounts of space
%around different classes of math symbols.
\begindesc
\bix^^{è¿ç®—ç¬¦//å·¨ç®—ç¬¦}
\threecolumns 15
\easy\ctsdoubledisplay bigcap {}
\ctsdoubledisplay bigcup {}
\ctsdoubledisplay bigodot {}
\ctsdoubledisplay bigoplus {}
\ctsdoubledisplay bigotimes {}
\ctsdoubledisplay bigsqcup {}
\ctsdoubledisplay biguplus {}
\ctsdoubledisplay bigvee {}
\ctsdoubledisplay bigwedge {}
\ctsdoubledisplay coprod {}
{\symbolspace = 42pt\basicdisplay {\hskip 26pt$\smallint$}%
   {\\smallint}\ddstrut}%
   \xrdef{\smallint} \pix\ctsidxref{smallint}
\ctsdoubledisplay int {}
\ctsdoubledisplay oint {}
\ctsdoubledisplay prod {}
\ctsdoubledisplay sum {}
}
\explain
è¿™äº›å‘½ä»¤æŽ’å°å„ç§å·¨ç®—ç¬¦ã€‚
\TeX\ åœ¨^{æ–‡å†…æ&nbsp;·å¼}ä¸­æŽ’å°å°å·å­—ç¬¦ï¼Œ
\minrefs{math mode}è€Œåœ¨^{é™ˆåˆ—æ&nbsp;·å¼}ä¸­æŽ’å°å¤§å·å­—ç¬¦.
å·¨ç®—ç¬¦æ˜¯ \TeX\ æ•°å­¦ç¬¦å·çš„å…¶ä¸­ä¸€\minref{ç±»}ã€‚
\TeX\ åœ¨ä¸åŒç±»æ•°å­¦ç¬¦å·é—´ç•™ä¸‹ä¸åŒå¤§å°çš„é—´éš”ã€‚

%The large operator symbols with `|big|' in their names are different
%from the corresponding binary operations (see \xref{binops}) such as
%|\cap| ($\cap$) since they usually appear at the beginning
%of a formula.  \TeX\ uses different spacing for a large operator
%than it does for a binary operation.
åç§°ä¸­å¸¦æœ‰ `|big|' çš„å·¨ç®—ç¬¦å’Œå¯¹åº”çš„äºŒå…ƒè¿ç®—ç¬¦%
ï¼ˆæ¯”å¦‚ |\cap| ($\cap$)ï¼Œè§\xref{binops}ï¼‰ä¸åŒï¼Œ
å›&nbsp;ä¸ºå®ƒä»¬é€šå¸¸å‡ºçŽ°å…¬å¼çš„å¼€å¤´ã€‚
\TeX\ ç»™å·¨ç®—ç¬¦ç•™ä¸‹çš„é—´éš”ä¸ŽäºŒå…ƒè¿ç®—ç¬¦çš„ä¸åŒã€‚

%Don't confuse `$\sum$' (|\sum|) with `$\Sigma$'^^|\Sigma| (|\Sigma|)
%or confuse `$\prod$' (|\prod|) with `$\Pi$' ^^|\Pi| (|\Pi|).
%|\Sigma| and |\Pi| produce capital Greek letters, which are smaller and
%have a different appearance.
ä¸è¦æ··æ·† `$\sum$' (|\sum|) å’Œ `$\Sigma$'^^|\Sigma| (|\Sigma|)ï¼Œ
æˆ–è€… `$\prod$' (|\prod|) å’Œ `$\Pi$' ^^|\Pi| (|\Pi|)ã€‚
|\Sigma| å’Œ |\Pi| æŽ’å°å¤§å†™å¸Œè…Šå­—æ¯ï¼Œå®ƒä»¬å°ºå¯¸æ›´å°ï¼Œå¤–è§‚ä¹Ÿä¸åŒã€‚

%A large operator can have ^{limits}.  The lower limit is specified as a
%subscript and the upper limit as a superscript.
å·¨ç®—ç¬¦å¯ä»¥å¸¦æœ‰^{æžé™}ã€‚ä¸‹æžé™ç”¨ä¸‹æ&nbsp;‡æŒ‡å®šï¼Œè€Œä¸Šæžé™ç”¨ä¸Šæ&nbsp;‡æŒ‡å®šã€‚

%\example
%$$\bigcap_{k=1}^r (a_k \cup b_k)$$
%|
%\dproduces
%$$\bigcap_{k=1}^r (a_k \cup b_k)$$
%\endexample
%\interexampleskip
%\example
%$${\int_0^\pi \sin^2 ax\,dx} = {\pi \over 2}$$
%|
%\dproduces
%$${\int_0^\pi \sin^2 ax\,dx} = {\pi \over 2}$$
%\endexample
%\enddesc
\example
$$\bigcap_{k=1}^r (a_k \cup b_k)$$
|
\dproduces
$$\bigcap_{k=1}^r (a_k \cup b_k)$$
\endexample
\interexampleskip
\example
$${\int_0^\pi \sin^2 ax\,dx} = {\pi \over 2}$$
|
\dproduces
$${\int_0^\pi \sin^2 ax\,dx} = {\pi \over 2}$$
\endexample
\enddesc

%\begindesc
%\cts limits {}
%\explain
%When it's in text style, \TeX\ normally places limits after a large operator.
%This command tells \TeX\ to place
%limits above and below a large operator rather than after it.
\begindesc
\cts limits {}
\explain
åœ¨æ–‡å†…æ&nbsp;·å¼ä¸­ï¼Œ\TeX\ é€šå¸¸å°†æžé™æ”¾åœ¨å·¨ç®—ç¬¦åŽè¾¹ã€‚
æ­¤å‘½ä»¤è®© \TeX\ å°†æžé™æ”¾åœ¨å·¨ç®—ç¬¦çš„ä¸Šè¾¹å’Œä¸‹è¾¹ï¼Œè€Œä¸æ˜¯åœ¨åŽè¾¹ã€‚

%If you specify more than one of |\limits|, |\nolimits|,
%and |\display!-limits|, the last command rules.
å¦‚æžœä½&nbsp;å¤šæ¬¡ä½¿ç”¨ |\limits|ã€|\nolimits| æˆ– |\display!-limits|ï¼Œ
ä»…æœ€åŽä¸€ä¸ªå‘½ä»¤ç”Ÿæ•ˆã€‚

%\example
%Suppose that $\bigcap\limits_{i=1}^Nq_i$ contains at least
%two elements.
%|
%\produces
%Suppose that $\bigcap\limits_{i=1}^Nq_i$ contains at least
%two elements.
%\endexample
%\enddesc
\example
Suppose that $\bigcap\limits_{i=1}^Nq_i$ contains at least
two elements.
|
\produces
Suppose that $\bigcap\limits_{i=1}^Nq_i$ contains at least
two elements.
\endexample
\enddesc

%\begindesc
%\cts nolimits {}
%\explain
%When it's in display
%style, \TeX\ normally places limits above and below a large operator.
%(The |\int| operator is an exception---\TeX\
%places limits for |\int| after the operator in all cases.)
%^^|\int//limits after|
%This command tells \TeX\ to place
%limits after a large operator rather than above and below it.
\begindesc
\cts nolimits {}
\explain
åœ¨é™ˆåˆ—æ&nbsp;·å¼ä¸­ï¼Œ\TeX\ é€šå¸¸å°†æžé™æ”¾åœ¨å·¨ç®—ç¬¦çš„ä¸Šè¾¹å’Œä¸‹è¾¹ã€‚%
ï¼ˆ|\int| ç®—ç¬¦æ˜¯ä¸€ä¸ªä¾‹å¤–â€”â€” \TeX\ æ€»æ˜¯å°†æžé™æ”¾åœ¨ç®—ç¬¦çš„åŽè¾¹ã€‚ï¼‰%
^^|\int//æžé™æ”¾åœ¨åŽé¢|
æ­¤å‘½ä»¤è®© \TeX\ å°†æžé™æ”¾åœ¨å·¨ç®—ç¬¦åŽè¾¹ï¼Œè€Œä¸æ˜¯ä¸Šè¾¹å’Œä¸‹è¾¹ã€‚

%If you specify more than one of |\limits|, |\nolimits|,
%and |\display!-limits|, the last command rules.
å¦‚æžœä½&nbsp;å¤šæ¬¡ä½¿ç”¨ |\limits|ã€|\nolimits| æˆ– |\display!-limits|ï¼Œ
ä»…æœ€åŽä¸€ä¸ªå‘½ä»¤ç”Ÿæ•ˆã€‚

%\example
%$$\bigcap\nolimits_{i=1}^Nq_i$$
%|
%\dproduces
%$$\bigcap\nolimits_{i=1}^Nq_i$$
%\endexample
%\enddesc
\example
$$\bigcap\nolimits_{i=1}^Nq_i$$
|
\dproduces
$$\bigcap\nolimits_{i=1}^Nq_i$$
\endexample
\enddesc

%\begindesc
%\cts displaylimits {}
%\explain
%This command tells \TeX\ to
%follow its normal rules for placement of limits:
%\olist\compact
%\li Limits on ^|\int| are placed after the operator.
%\li Limits on other large operators are placed after the
%operator in text style.
%\li Limits on other large operators are placed above and below the operator
%in display style.
%\endolist
%It's usually simpler to use |\limits| or |\nolimits|
%to produce a specific effect, but |\display!-limits| is sometimes
%useful in \minref{macro} definitions.
\begindesc
\cts displaylimits {}
\explain
æ­¤å‘½ä»¤è®© \TeX\ æŒ‰ç…§é€šå¸¸æ–¹å¼æ”¾ç½®æžé™ï¼š
\olist\compact
\li ^|\int| ç®—ç¬¦çš„æžé™æ€»æ”¾åœ¨ç®—ç¬¦åŽè¾¹ã€‚%
\footnote{è¯‘æ³¨ï¼šæ­¤å¤„ä¼¼ä¹Žæœ‰è¯¯ï¼Œåœ¨ |\displaylimits| ä¸‹ ^|\int| å’Œå…¶ä»–ç®—ç¬¦åº”è¯¥æœ‰ç›¸åŒçš„è¡¨çŽ°ã€‚}
\li åœ¨æ–‡å†…æ&nbsp;·å¼ä¸­ï¼Œå…¶ä»–å·¨ç®—ç¬¦çš„æžé™æ”¾åœ¨ç®—ç¬¦çš„åŽè¾¹ã€‚
\li åœ¨é™ˆåˆ—æ&nbsp;·å¼ä¸­ï¼Œå…¶ä»–å·¨ç®—ç¬¦çš„æžé™æ”¾åœ¨ç®—ç¬¦çš„ä¸Šè¾¹å’Œä¸‹è¾¹ã€‚
\endolist
ç”¨ |\limits| æˆ– |\nolimits| æ¥æŽ’å°ç‰¹å®šæ•ˆæžœæ›´ä¸ºç®€å•ï¼Œ
ä½† |\display!-limits| åœ¨\minref{å®}å®šä¹‰ä¸­æœ‰æ—¶ä¼šç”¨åˆ°ã€‚

%Note that \plainTeX\ defines ^|\int| as a macro that sets |\nolimits|,
%so |\int\displaylimits| in text style restores the |\limits|
%convention.
æ³¨æ„ \plainTeX\ åœ¨å®šä¹‰ ^|\int| æ—¶å°±å¸¦æœ‰ |\nolimits|ï¼Œ
å›&nbsp;æ­¤æ–‡å†…æ&nbsp;·å¼çš„ |\int\displaylimits| å°†æ¢å¤ |\limits| çº¦å®šã€‚%
\footnote{è¯‘æ³¨ï¼šæ­¤å¤„ä¼¼ä¹Žæœ‰è¯¯ï¼Œåœ¨æ–‡å†…æ&nbsp;·å¼ä¸­ï¼Œ|\int\displaylimits| çš„æžé™åº”è¯¥è¿˜æ˜¯åœ¨åŽè¾¹ã€‚}

%If you specify more than one of |\limits|, |\nolimits|,
%and |\display!-limits|, the last command rules.
å¦‚æžœä½&nbsp;å¤šæ¬¡ä½¿ç”¨ |\limits|ã€|\nolimits| æˆ– |\display!-limits|ï¼Œ
ä»…æœ€åŽä¸€ä¸ªå‘½ä»¤ç”Ÿæ•ˆã€‚

%\example
%$$a(\lambda) = {1 \over {2\pi}} \int\displaylimits
%_{-\infty}^{+\infty} f(x)e^{-i\lambda x}\,dx$$
%|
%\dproduces
%$$a(\lambda) = {1 \over {2\pi}} \int\displaylimits
%_{-\infty}^{+\infty} f(x)e^{-i\lambda x}\,dx$$
\example
$$a(\lambda) = {1 \over {2\pi}} \int\displaylimits
_{-\infty}^{+\infty} f(x)e^{-i\lambda x}\,dx$$
|
\dproduces
$$a(\lambda) = {1 \over {2\pi}} \int\displaylimits
_{-\infty}^{+\infty} f(x)e^{-i\lambda x}\,dx$$

%\eix^^{operators//large}
%\endexample
%\enddesc
\eix^^{è¿ç®—ç¬¦//å·¨ç®—ç¬¦}
\endexample
\enddesc


%==========================================================================
%\subsection {Punctuation}
\subsection {æ&nbsp;‡ç‚¹}

%\begindesc
%\bix^^{punctuation in math formulas}
%\cts cdotp {}
%\cts ldotp {}
%\explain
%These two commands respectively produce a centered dot and a dot
%positioned on the \minref{baseline}.  They are valid only in math
%\minref{mode}.  \TeX\ treats them as punctuation, putting no extra space in
%front of them but a little extra space after them.
%In contrast, \TeX\ puts an equal amount of space on both sides
%of a centered dot generated by the ^|\cdot| command (\xref \cdot).
%\example
%$x \cdotp y \quad x \ldotp y \quad x \cdot y$
%|
%\produces
%$x \cdotp y \quad x \ldotp y \quad x \cdot y$
%\endexample
%\enddesc
\begindesc
\bix^^{æ•°å­¦å…¬å¼ä¸­çš„æ&nbsp;‡ç‚¹}
\cts cdotp {}
\cts ldotp {}
\explain
è¿™ä¸¤ä¸ªå‘½ä»¤åˆ†åˆ«æŽ’å°å±…ä¸­çš„åœ†ç‚¹å’Œåœ¨\minref{åŸºçº¿}ä¸Šçš„åœ†ç‚¹ã€‚
å®ƒä»¬ä»…å¯ç”¨äºŽæ•°å­¦\minref{æ¨¡å¼}ä¸­ã€‚
\TeX\ å°†å®ƒä»¬è§†ä¸ºæ&nbsp;‡ç‚¹ï¼Œåœ¨å‰é¢ä¸ç•™é—´éš”è€Œåœ¨åŽé¢ç•™ä¸‹ä¸€ç‚¹é—´éš”ã€‚
ä¸Žæ­¤ç›¸åï¼Œå¯¹äºŽç”¨ ^|\cdot| å‘½ä»¤ï¼ˆ\xref\cdot ï¼‰ç”Ÿæˆçš„å±…ä¸­åœ†ç‚¹ï¼Œ
\TeX\ åœ¨å…¶ä¸¤ä¾§ç•™ä¸‹ç›¸åŒå¤§å°çš„é—´éš”ã€‚
\example
$x \cdotp y \quad x \ldotp y \quad x \cdot y$
|
\produces
$x \cdotp y \quad x \ldotp y \quad x \cdot y$
\endexample
\enddesc

%\begindesc
%\cts colon {}
%\explain
%This command produces a colon punctation symbol.
%It is valid only in math mode.
%The difference between |\colon| and the colon character (|:|) is that
%`|:|' is an operator, so \TeX\ puts extra space to the left of it whereas
%it doesn't put extra space to the left of |\colon|.
%\example
%$f \colon t \quad f : t$
%|
%\produces
%$f \colon t \quad f : t$
\begindesc
\cts colon {}
\explain
æ­¤å‘½ä»¤æŽ’å°ä¸€ä¸ªå†’å·æ&nbsp;‡ç‚¹ï¼Œå®ƒåªèƒ½ç”¨åœ¨æ•°å­¦æ¨¡å¼ä¸­ã€‚
å†’å·æ&nbsp;‡ç‚¹ |\colon| å’Œå†’å·å­—ç¬¦(|:|)çš„åŒºåˆ«åœ¨äºŽï¼Œ
`|:|' æ˜¯ä¸€ä¸ªè¿ç®—ç¬¦ï¼Œå›&nbsp;æ­¤ \TeX\ åœ¨å…¶å·¦ä¾§ç•™ä¸‹é¢å¤–é—´éš”ï¼Œ
ç„¶è€Œåœ¨ |\colon| å·¦ä¾§å´ä¸ç•™é¢å¤–é—´éš”ã€‚
\example
$f \colon t \quad f : t$
|
\produces
$f \colon t \quad f : t$

%\eix^^{punctuation in math formulas}
%\endexample
%\enddesc
\eix^^{æ•°å­¦å…¬å¼ä¸­çš„æ&nbsp;‡ç‚¹}
\endexample
\enddesc


%==========================================================================
%\secondprinting{\vfill\eject\null\vglue-30pt\vskip0pt}
%\section {Superscripts and subscripts}
\section {ä¸Šæ&nbsp;‡å’Œä¸‹æ&nbsp;‡}

%\begindesc
%\margin{Two groups of commands have been combined here.}
%\bix^^{superscripts}
%\bix^^{subscripts}
%\secondprinting{\vglue-12pt}
%\makecolumns 4/2:
%\easy\ctsact _ \xrdef{@underscore} {\&lt;argument&gt;}
%\cts sb {\&lt;argument&gt;}
%\ctsact ^ \xrdef{@hat} {\&lt;argument&gt;}
%\cts sp {\&lt;argument&gt;}
%\secondprinting{\vglue-4pt}
%\explain
%The commands in each column are equivalent.  The commands in the first
%column typeset \&lt;argument&gt; as a subscript, and those in the second
%column typeset \&lt;argument&gt; as a superscript.  The |\sb| and |\sp|
%commands are mainly useful if you're working on a terminal that lacks an
%underscore or caret, or if you've redefined `|_|' or `|^|' and need
%access to the original definition.  These commands are also used for
%setting lower and upper limits on summations and integrals.  ^^{lower
%limits} ^^{upper limits}
\begindesc
\margin{Two groups of commands have been combined here.}
\bix^^{ä¸Šæ&nbsp;‡}
\bix^^{ä¸‹æ&nbsp;‡}
\secondprinting{\vglue-12pt}
\makecolumns 4/2:
\easy\ctsact _ \xrdef{@underscore} {\&lt;argument&gt;}
\cts sb {\&lt;argument&gt;}
\ctsact ^ \xrdef{@hat} {\&lt;argument&gt;}
\cts sp {\&lt;argument&gt;}
\secondprinting{\vglue-4pt}
\explain
å„æ&nbsp;çš„ä¸¤ä¸ªå‘½ä»¤éƒ½æ˜¯ç­‰ä»·çš„ã€‚ç¬¬ä¸€æ&nbsp;çš„å‘½ä»¤å°† \&lt;argument&gt; æŽ’ç‰ˆä¸ºä¸‹æ&nbsp;‡ï¼Œ
è€Œç¬¬äºŒæ&nbsp;çš„å‘½ä»¤å°† \&lt;argument&gt; æŽ’ç‰ˆä¸ºä¸Šæ&nbsp;‡ã€‚
|\sb| å’Œ |\sp| å‘½ä»¤ä¸»è¦ç”¨äºŽæ—&nbsp;æ³•ä½¿ç”¨ä¸‹åˆ’çº¿å’Œæ’å…¥ç¬¦çš„ç»ˆç«¯ä¸­ï¼Œ
æˆ–è€…ç”¨åœ¨é‡æ–°å®šä¹‰äº† `|_|' or `|^|' ä½†éœ€è¦å…¶åŽŸå§‹å®šä¹‰çš„æƒ…å†µä¸‹ã€‚
è¿™äº›å‘½ä»¤ä¹Ÿç”¨äºŽè®¾å®šæ±‚å’Œå·å’Œç§¯åˆ†å·çš„ä¸‹æžé™å’Œä¸Šæžé™ã€‚
^^{ä¸‹æžé™} ^^{ä¸Šæžé™}

%If a subscript or superscript is not a single \minref{token}, you need
%to enclose it in a \minref{group}.  \TeX\ does not prioritize subscripts
%or superscripts, so it will reject formulas such as |a_i_j|, |a^i^j|, or
%|a^i_j|.
å¦‚æžœä¸‹æ&nbsp;‡æˆ–ä¸Šæ&nbsp;‡ä¸æ˜¯å•ä¸ª\minref{è®°å·}ï¼Œä½&nbsp;éœ€è¦å°†å®ƒæ”¾åœ¨\minref{ç¼–ç»„}ä¸­ã€‚
\TeX\ å¹¶ä¸å¤„ç†ä¸‹æ&nbsp;‡å’Œä¸Šæ&nbsp;‡çš„ä¼˜å…ˆçº§ï¼Œ
å›&nbsp;æ­¤å®ƒå°†æ‹’ç»ç±»ä¼¼ |a_i_j|ã€|a^i^j| æˆ– |a^i_j| çš„å…¬å¼ã€‚

%Subscripts and superscripts are normally typeset in ^{script style}, or
%in ^{scriptscript style} if they are second-order, e.g., a subscript on
%a subscript or a superscript on a a subscript.  You can set \emph{any}
%text in a math formula in a script or scriptscript \minref{style} with
%the ^|\scriptstyle| and ^|\scriptscriptstyle| commands (\xref
%\scriptscriptstyle).
ä¸‹æ&nbsp;‡å’Œä¸Šæ&nbsp;‡æŽ’ç‰ˆæ—¶é€šå¸¸ç”¨^{æ&nbsp;‡å·æ&nbsp;·å¼}ï¼Œæˆ–è€…^{å°æ&nbsp;‡å·æ&nbsp;·å¼}ï¼Œ
å¦‚æžœå®ƒä»¬æ˜¯äºŒé˜¶æ&nbsp;‡å·ï¼Œæ¯”å¦‚ä¸‹æ&nbsp;‡ä¸­çš„ä¸‹æ&nbsp;‡æˆ–ä¸‹æ&nbsp;‡ä¸­çš„ä¸Šæ&nbsp;‡ã€‚
åˆ©ç”¨ ^|\scriptstyle| å’Œ ^|\scriptscriptstyle| å‘½ä»¤ï¼ˆ\xref\scriptscriptstyle ï¼‰ï¼Œ
ä½&nbsp;å¯ä»¥å°†æ•°å­¦å…¬å¼çš„\emph{ä»»ä½•}æ–‡æœ¬è®¾ä¸ºæ&nbsp;‡å·æˆ–å°æ&nbsp;‡å·\minref{æ&nbsp;·å¼}ã€‚

%You can apply a subscript or superscript to any of the commands that
%produce named mathematical functions in roman type (see
%\xref{namedfns}).  In certain cases (again, see \xref{namedfns}) the
%subscript or superscript appears directly above or under the function
%name as shown in the examples of ^|\lim| and ^|\det| below.
å¯¹ä»»ä½•ä»¥ç½—é©¬å­—ä½“æŽ’å°å‘½åæ•°å­¦å‡½æ•°ï¼ˆè§\xref{namedfns}ï¼‰çš„å‘½ä»¤ï¼Œ
ä½&nbsp;éƒ½å¯ä»¥ç»™å®ƒæ·»åŠ&nbsp;ä¸‹æ&nbsp;‡å’Œä¸Šæ&nbsp;‡ã€‚
åœ¨æŸäº›æƒ…å½¢ä¸­ï¼ˆåŒæ&nbsp;·è§\xref{namedfns}ï¼‰ï¼Œ
ä¸‹æ&nbsp;‡å’Œä¸Šæ&nbsp;‡åˆ†åˆ«å‡ºçŽ°åœ¨å‡½æ•°åçš„ä¸‹è¾¹å’Œä¸Šè¾¹ï¼Œ
å¦‚ä¸‹é¢ä¾‹å­ä¸­çš„ ^|\lim| å’Œ ^|\det| æ‰€ç¤ºã€‚

%\example
%$x_3 \quad t_{\max} \quad a_{i_k} \quad \sum_{i=1}^n{q_i}
%   \quad x^3\quad e^{t \cos\theta}\quad r^{x^2}\quad
%   \int_0^\infty{f(x)\,dx}$
%$$\lim_{x\leftarrow0}f(x)\qquad\det^{z\in A}\qquad\sin^2t$$
%|
%\produces
%\secondprinting{\divide\abovedisplayskip by 2}
%$x_3 \quad t_{\max} \quad a_{i_k} \quad \sum_{i=1}^n{q_i}
%   \quad x^3\quad e^{t \cos\theta}\quad r^{x^2}\quad
%   \int_0^\infty{f(x)\,dx}$
%$$\lim_{x \leftarrow 0} f(x)\qquad
%   \det^{z \in A}\qquad \sin^2 t$$
\example
$x_3 \quad t_{\max} \quad a_{i_k} \quad \sum_{i=1}^n{q_i}
   \quad x^3\quad e^{t \cos\theta}\quad r^{x^2}\quad
   \int_0^\infty{f(x)\,dx}$
$$\lim_{x\leftarrow0}f(x)\qquad\det^{z\in A}\qquad\sin^2t$$
|
\produces
%\secondprinting{\divide\abovedisplayskip by 2}
$x_3 \quad t_{\max} \quad a_{i_k} \quad \sum_{i=1}^n{q_i}
   \quad x^3\quad e^{t \cos\theta}\quad r^{x^2}\quad
   \int_0^\infty{f(x)\,dx}$
$$\lim_{x \leftarrow 0} f(x)\qquad
   \det^{z \in A}\qquad \sin^2 t$$

%\eix^^{superscripts}
%\eix^^{subscripts}
%\endexample
%\enddesc
\eix^^{ä¸Šæ&nbsp;‡}
\eix^^{ä¸‹æ&nbsp;‡}
\endexample
\enddesc

%\secondprinting{\vfill\eject}

%==========================================================================
%\subsection {Selecting and using styles}
\subsection {é€‰ç”¨æ&nbsp;·å¼}

%\begindesc
%\bix^^{styles}
%\cts textstyle {}
%\cts scriptstyle {}
%\cts scriptscriptstyle {}
%\cts displaystyle {}
%\explain
%^^{text style} ^^{script style} ^^{scriptscript style} ^^{display style}
%These commands override the normal \minref{style} and hence the
%font that \TeX\ uses in setting a formula.  Like
%font-setting commands such as |\it|, they are in
%effect until the end of the group containing them.
%They are useful when \TeX's choice of style is inappropriate for the formula
%you happen to be setting.
%\example
%$t+{\scriptstyle t + {\scriptscriptstyle t}}$
%|
%\produces
%$t+{\scriptstyle t + {\scriptscriptstyle t}}$
%\endexample
%\enddesc
\begindesc
\bix^^{æ&nbsp;·å¼}
\cts textstyle {}
\cts scriptstyle {}
\cts scriptscriptstyle {}
\cts displaystyle {}
\explain
^^{æ–‡æœ¬æ&nbsp;·å¼} ^^{æ&nbsp;‡å·æ&nbsp;·å¼} ^^{å°æ&nbsp;‡å·æ&nbsp;·å¼} ^^{é™ˆåˆ—æ&nbsp;·å¼}
è¿™äº›å‘½ä»¤è¦†ç›– \TeX\ æŽ’ç‰ˆå…¬å¼æ—¶é€šå¸¸ä½¿ç”¨çš„\minref{æ&nbsp;·å¼}åŠå…¶å­—ä½“ã€‚
å¦‚åŒç±»ä¼¼ |\it| çš„å­—ä½“è®¾ç½®å‘½ä»¤ï¼Œå®ƒä»¬åœ¨å…¶æ‰€åœ¨ç¼–ç»„ç»“æŸå‰ä¸€ç›´æœ‰æ•ˆã€‚
å½“ \TeX\ ç»™ä½&nbsp;è¦æŽ’ç‰ˆçš„å…¬å¼é€‰ç”¨äº†ä¸åˆé€‚çš„æ&nbsp;·å¼æ—¶ï¼Œä½&nbsp;å¯ä»¥ä½¿ç”¨è¿™äº›å‘½ä»¤ã€‚
\example
$t+{\scriptstyle t + {\scriptscriptstyle t}}$
|
\produces
$t+{\scriptstyle t + {\scriptscriptstyle t}}$
\endexample
\enddesc

%\begindesc
%\cts mathchoice {%
%   \rqbraces{\&lt;math$_1$&gt;}
%   \rqbraces{\&lt;math$_2$&gt;}
%   \rqbraces{\&lt;math$_3$&gt;}
%   \rqbraces{\&lt;math$_4$&gt;}}
%\explain
%This command tells \TeX\ to typeset one of the subformulas
%\&lt;math$_1$&gt;, \&lt;math$_2$&gt;, \&lt;math$_3$&gt;, or \&lt;math$_4$&gt;, making its choice
%according to the current \minref{style}.
%That is, if \TeX\ is in
%display style it sets the |\mathchoice| as \&lt;math$_1$&gt;; in text style it sets
%it as \&lt;math$_2$&gt;; in script style it sets it as \&lt;math$_3$&gt;;
%and in scriptscript style it sets it as \&lt;math$_4$&gt;.
%\example
%\def\mc{{\mathchoice{D}{T}{S}{SS}}}
%The strange formula $\mc_{\mc_\mc}$ illustrates a
%mathchoice.
%|
%\produces
%\def\mc{{\mathchoice{D}{T}{S}{SS}}}
%The strange formula $\mc_{\mc_\mc}$ illustrates a
%mathchoice.
%\endexample
%\enddesc
\begindesc
\cts mathchoice {%
   \rqbraces{\&lt;math$_1$&gt;}
   \rqbraces{\&lt;math$_2$&gt;}
   \rqbraces{\&lt;math$_3$&gt;}
   \rqbraces{\&lt;math$_4$&gt;}}
\explain
æ­¤å‘½ä»¤è®© \TeX\ æ&nbsp;¹æ®å½“å‰\minref{æ&nbsp;·å¼}é€‰æ‹©å¹¶æŽ’ç‰ˆå…¶ä¸­ä¸€ä¸ªå­å…¬å¼
\&lt;math$_1$&gt;ã€\&lt;math$_2$&gt;ã€\&lt;math$_3$&gt; æˆ– \&lt;math$_4$&gt;ã€‚
ä¹Ÿå°±æ˜¯è¯´ï¼Œå¦‚æžœåœ¨é™ˆåˆ—æ&nbsp;·å¼ä¸­ï¼Œ\TeX\ å°† |\mathchoice| æŽ’ç‰ˆä¸º \&lt;math$_1$&gt;ï¼›
åœ¨æ–‡æœ¬æ&nbsp;·å¼ä¸­æŽ’ç‰ˆä¸º \&lt;math$_2$&gt;ï¼Œåœ¨æ&nbsp;‡å·æ&nbsp;·å¼ä¸­æŽ’ç‰ˆä¸º \&lt;math$_3$&gt;ï¼›
è€Œåœ¨å°æ&nbsp;‡å·æ&nbsp;·å¼ä¸­æŽ’ç‰ˆä¸º \&lt;math$_4$&gt;ã€‚
\example
\def\mc{{\mathchoice{D}{T}{S}{SS}}}
The strange formula $\mc_{\mc_\mc}$ illustrates a
mathchoice.
|
\produces
\def\mc{{\mathchoice{D}{T}{S}{SS}}}
The strange formula $\mc_{\mc_\mc}$ illustrates a
mathchoice.
\endexample
\enddesc

%\begindesc
%\cts mathpalette {\&lt;argument$_1$&gt; \&lt;argument$_2$&gt;}
%\explain
%^^{math symbols}
%This command provides a convenient way of
%producing a math construct that works in all four \minref{style}s.
%To use it, you'll normally need to define an additional macro,
%which we'll call |\build|.
%The call on |\math!-palette| should then have the form
%|\mathpalette|\allowbreak|\build|\&lt;argument&gt;.
\begindesc
\cts mathpalette {\&lt;argument$_1$&gt; \&lt;argument$_2$&gt;}
\explain
^^{æ•°å­¦ç¬¦å·}
æ­¤å‘½ä»¤æä¾›ä¸€ç§ç”Ÿæˆé€‚ç”¨äºŽå››ç§\minref{æ&nbsp;·å¼}çš„æ•°å­¦ç»“æž„çš„ç®€ä¾¿æ–¹æ³•ã€‚%
\footnote{è¯‘æ³¨ï¼šè¯¥å®å®šä¹‰ä¸º
|\def\mathpalette#1#2{\mathchoice{#1\displaystyle{#2}}|\break
|{#1\textstyle{#2}}{#1\scriptstyle{#2}}{#1\scriptscriptstyle{#2}}}|ã€‚}
è¦ä½¿ç”¨å®ƒï¼Œé€šå¸¸ä½&nbsp;éœ€è¦å®šä¹‰ä¸€ä¸ªé¢å¤–çš„å®ï¼Œå‡è®¾æˆ‘ä»¬ç§°å®ƒä¸º |\build|ã€‚
è°ƒç”¨ |\math!-palette| å°±åº”è¯¥ç”¨
|\mathpalette|\allowbreak|\build|\&lt;argument&gt; è¿™ç§å½¢å¼ã€‚


%|\build| tests what style \TeX\ is in and typesets \&lt;argu\-ment&gt; accordingly.
%It should be defined to have two parameters.
%When you call |\math!-palette|, it will in turn call |\build|,
%with |#1| being a
%command that selects the current style and |#2| being \&lt;argument&gt;.
%Thus, within the definition of |\build| you can typeset something
%in the current style by preceding it with `|#1|'.
%See \knuth{page~360} for examples of using |\mathpalette|
%and \knuth{page~151} for a further explanation of how it works.
|\build| æµ‹è¯• \TeX\ ä½äºŽä½•ç§æ&nbsp;·å¼ï¼Œå¹¶ç›¸åº”åœ°æŽ’ç‰ˆ \&lt;argu\-ment&gt;ã€‚
å®ƒåº”è¯¥å®šä¹‰ä¸ºæœ‰ä¸¤ä¸ªå‚æ•°ã€‚
å½“ä½&nbsp;è°ƒç”¨ |\math!-palette| æ—¶ï¼Œå®ƒä»¥ |#1| ä¸ºé€‰æ‹©æ&nbsp;·å¼çš„å‘½ä»¤ï¼Œ
|#2| ä¸º \&lt;argument&gt; è½¬è€Œè°ƒç”¨ |\build|ã€‚
å›&nbsp;æ­¤ï¼Œåœ¨ |\build| çš„å®šä¹‰ä¸­ï¼Œ
é€šè¿‡å°†æŸäº›ä¸œè¥¿æ”¾åœ¨ `|#1|' å‰é¢ï¼Œå°±å¯ä»¥ç”¨å½“å‰æ&nbsp;·å¼æŽ’ç‰ˆå®ƒã€‚
åœ¨\knuth{ç¬¬~360~é¡µ}ä¸­æœ‰å¦‚ä½•ä½¿ç”¨ |\mathpalette| çš„ä¾‹å­ï¼Œ
è€Œåœ¨\knuth{ç¬¬~151~é¡µ}ä¸­æœ‰å®ƒå¦‚ä½•è¿ä½œçš„è¿›ä¸€æ­¥è§£é‡Šã€‚

%\eix^^{styles}
%\enddesc
\eix^^{æ&nbsp;·å¼}
\enddesc

%==========================================================================
%\section {Compound symbols}
\section {å¤åˆç¬¦å·}

%==========================================================================
%\subsection {Math accents}
\subsection {æ•°å­¦é‡éŸ³}

%\begindesc
%\xrdef{mathaccent}
%^^{accents}
%^^{math//accents}
%%
%\easy\ctsx acute {^{acute accent} as in $\acute x$}
%\ctsx b {^{bar-under accent} as in $\b x$}
%\ctsx bar {^{bar accent} as in $\bar x$}
%\ctsx breve {^{breve accent} as in $\breve x$}
%\ctsx check {^{check accent} as in $\check x$}
%\ctsx ddot {^{double dot accent} as in $\ddot x$}
%\ctsx dot {^{dot accent} as in $\dot x$}
%\ctsx grave {^{grave accent} as in $\grave x$}
%\ctsx hat {^{hat accent} as in $\hat x$}
%\ctsx widehat {^{wide hat accent} as in $\widehat {x+y}$}
%\ctsx tilde {^{tilde accent} as in $\tilde x$}
%\ctsx widetilde {^{wide tilde accent} as in $\widetilde {z+a}$}
%\ctsx vec {^{vector accent} as in $\vec x$}
%\explain
%These commands produce accent marks in math formulas.  You'll ordinarily
%need to leave a space after any one of them.
%A wide accent can be applied to a multicharacter subformula;
%\TeX\ will center the accent over the subformula.
%The other accents are usefully applied only to a single character.
\begindesc
\xrdef{mathaccent}
^^{é‡éŸ³}
^^{æ•°å­¦//æ•°å­¦é‡éŸ³}
%
\easy\ctsx acute {^{é”éŸ³ç¬¦}ï¼Œå¦‚åŒ $\acute x$}
\ctsx b {^{ä¸‹çº¿ç¬¦}ï¼Œå¦‚åŒ $\b x$}
\ctsx bar {^{ä¸Šçº¿ç¬¦}ï¼Œå¦‚åŒ $\bar x$}
\ctsx breve {^{çŸ­éŸ³ç¬¦}ï¼Œå¦‚åŒ $\breve x$}
\ctsx check {^{æŠ‘æ‰¬ç¬¦}ï¼Œå¦‚åŒ $\check x$}
\ctsx ddot {^{åŒç‚¹ç¬¦}ï¼Œå¦‚åŒ $\ddot x$}
\ctsx dot {^{ä¸Šç‚¹ç¬¦}ï¼Œå¦‚åŒ $\dot x$}
\ctsx grave {^{é’éŸ³ç¬¦}ï¼Œå¦‚åŒ $\grave x$}
\ctsx hat {^{å°–è§’ç¬¦}ï¼Œå¦‚åŒ $\hat x$}
\ctsx widehat {^{å®½å°–è§’ç¬¦}ï¼Œå¦‚åŒ $\widehat {x+y}$}
\ctsx tilde {^{æ³¢æµªç¬¦}ï¼Œå¦‚åŒ $\tilde x$}
\ctsx widetilde {^{å®½æ³¢æµªç¬¦}ï¼Œå¦‚åŒ $\widetilde {z+a}$}
\ctsx vec {^{å‘é‡ç¬¦}ï¼Œå¦‚åŒ $\vec x$}
\explain
è¿™äº›å‘½ä»¤åœ¨æ•°å­¦å…¬å¼ä¸ŠæŽ’å°é‡éŸ³æ&nbsp;‡è®°ã€‚ä½&nbsp;é€šå¸¸éœ€è¦åœ¨å®ƒä»¬åŽé¢ç•™ä¸‹ç©ºæ&nbsp;¼ã€‚
å®½é‡éŸ³å¯ä»¥åº”ç”¨åˆ°å¤šå­—ç¬¦å­å…¬å¼ä¸­ï¼›\TeX\ å°†æŠŠé‡éŸ³æ”¾åœ¨å­å…¬å¼çš„ä¸­é—´ã€‚
å…¶ä»–é‡éŸ³ä»…åœ¨åº”ç”¨åˆ°å•ä¸ªå­—ç¬¦æ—¶æ‰æœ‰ç”¨ã€‚

%\example
%$\dot t^n \qquad \widetilde{v_1 + v_2}$
%|
%\produces
%$\dot t^n \qquad \widetilde{v_1 + v_2}$
%\endexample
\example
$\dot t^n \qquad \widetilde{v_1 + v_2}$
|
\produces
$\dot t^n \qquad \widetilde{v_1 + v_2}$
\endexample

%\begindesc
%\cts mathaccent {\&lt;mathcode&gt;}
%\explain
%This command tells \TeX\ to typeset a math accent
%whose family and character code are given by \&lt;mathcode&gt;.  (\TeX\ ignores
%the class of the \minref{mathcode}.)
%See \knuth{Appendix~G} for the details of how \TeX\ positions such an accent.
%The usual way to use |\mathaccent| is to put it in a macro definition
%that gives a name to a math accent.
%\example
%\def\acute{\mathaccent "7013}
%|
%\endexample
%\enddesc
\begindesc
\cts mathaccent {\&lt;mathcode&gt;}
\explain
æ­¤å‘½ä»¤è®© \TeX\ æŽ’ç‰ˆå­—ä½“æ—å’Œå­—ç¬¦ç¼–ç&nbsp;ç”± \&lt;mathcode&gt; ç»™å‡ºçš„æ•°å­¦é‡éŸ³ã€‚%
ï¼ˆ\TeX\ å¿½ç•¥\minref{æ•°å­¦ç&nbsp;}ä¸­çš„ç±»ã€‚ï¼‰
è¯·å‚é˜…\knuth{é™„å½•~G}å¯¹ \TeX\ å¦‚ä½•æ”¾ç½®è¯¥é‡éŸ³çš„è¯¦ç»†ä»‹ç»ã€‚
ç»å¸¸å°† |\mathaccent| æ”¾åœ¨å®å®šä¹‰ä¸­ï¼Œä»¥ç»™æ•°å­¦é‡éŸ³ä¸€ä¸ªåç§°ã€‚
\example
\def\acute{\mathaccent "7013}
|
\endexample
\enddesc

%\see ``Accents'' (\xref {accents}).
%\enddesc
\see ``Accents''ï¼ˆ\xref {accents}ï¼‰ã€‚
\enddesc

%==========================================================================
%\subsection {Fractions and other stacking operations}
\subsection {åˆ†å¼å’Œå…¶ä»–å&nbsp;†å&nbsp;è¿ç®—}

%\begindesc
%\bix^^{fractions}
%\bix^^{stacking subformulas}
%\easy\cts over {}
%\cts atop {}
%\cts above {\&lt;dimen&gt;}
%\cts choose {}
%\cts brace {}
%\cts brack {}
%\explain
%{\def\fri{\&lt;formula$_1$&gt;}%
%\def\frii{\&lt;formula$_2$&gt;}%
%These commands stack one subformula on top of another one.  We will explain how
%|\over| works, and then relate the other commands to it.
\begindesc
\bix^^{åˆ†å¼}
\bix^^{å&nbsp;†å&nbsp;å­å…¬å¼}
\easy\cts over {}
\cts atop {}
\cts above {\&lt;dimen&gt;}
\cts choose {}
\cts brace {}
\cts brack {}
\explain
{\def\fri{\&lt;formula$_1$&gt;}%
\def\frii{\&lt;formula$_2$&gt;}%
è¿™äº›å‘½ä»¤å°†ä¸€ä¸ªå­å…¬å¼å&nbsp;†æ”¾åœ¨å¦ä¸€ä¸ªå­å…¬å¼ä¹‹ä¸Šã€‚
æˆ‘ä»¬å°†è§£é‡Š |\over| å¦‚ä½•ä½œç”¨ï¼Œç„¶åŽè¯´æ˜Žå…¶ä»–å‘½ä»¤ä¸Žå®ƒçš„å…³ç³»ã€‚

%|\over| is the command that you'd normally use to produce a fraction.
%^^{fractions//produced by \b\tt\\over\e}
%If you write something in one of the following forms:
%\csdisplay
%$$!fri\over!frii$$
%$!fri\over!frii$
%\left!&lt;delim&gt;!fri\over!frii\right!&lt;delim&gt;
%{!fri\over!frii}
%|
%you'll get a fraction with numerator \fri\  and denominator \&lt;for\-mu\-la$_2$&gt;,
%i.e., \fri\ over \frii.
%In the first three of
%these forms the |\over| is not implicitly contained in a group;
%it absorbs
%everything to its left and to its right until it comes to a boundary,
%namely, the beginning or end of a group.
|\over| å‘½ä»¤é€šå¸¸ç”¨äºŽæŽ’å°åˆ†å¼ã€‚
^^{åˆ†å¼//ç”¨ \b\tt\\over\e ç”Ÿæˆ}
å¦‚æžœä½&nbsp;æŒ‰ä¸‹é¢å‡&nbsp;ç§å½¢å¼ä¹‹ä¸€æ’°å†™ï¼š
\csdisplay
$$!fri\over!frii$$
$!fri\over!frii$
\left!&lt;delim&gt;!fri\over!frii\right!&lt;delim&gt;
{!fri\over!frii}
|
ä½&nbsp;å°†å¾—åˆ°åˆ†å­ä¸º \fri\ åˆ†æ¯ä¸º \&lt;for\-mu\-la$_2$&gt; çš„åˆ†å¼ï¼Œ
å³ \fri\ é™¤ä»¥ \frii ã€‚
åœ¨å‰é¢ä¸‰ç§å½¢å¼ä¸­ï¼Œ|\over| éžæ˜¾å¼åœ°åŒ…å«åœ¨ä¸€ä¸ªç¼–ç»„ä¸­ï¼›
å®ƒå¸æ”¶å·¦è¾¹å’Œå³è¾¹çš„å†…å®¹ç›´åˆ°é‡åˆ°è¾¹ç•Œï¼Œå³ç¼–ç»„çš„å¼€å¤´å’Œç»“å°¾ã€‚

%You can't use |\over| or any of the other commands in this group
%more than once in a formula.
%Thus a formula such as:
%\csdisplay
%$$a \over n \choose k$$
%|
%isn't legal.
%This is not a severe restriction because
%you can always enclose one of the commands in braces.
%The reason for the restriction is that if you had two of these commands
%in a single formula, \TeX\ wouldn't know how to group them.
ä½&nbsp;ä¸å¯ä»¥åœ¨ä¸€ä¸ªå…¬å¼ä¸­å¤šæ¬¡ä½¿ç”¨ |\over| æˆ–è¿™æ‰¹å‘½ä»¤çš„å…¶ä»–å‘½ä»¤ã€‚
å›&nbsp;æ­¤ä¸‹é¢çš„å…¬å¼ï¼š
\csdisplay
$$a \over n \choose k$$
|
æ˜¯ä¸åˆæ³•çš„ã€‚è¿™ä¸æ˜¯ä»€ä¹ˆä¸¥é‡çš„é™åˆ¶ï¼Œå›&nbsp;ä¸ºä½&nbsp;æ€»å¯ä»¥å°†å…¶ä¸­ä¸€ä¸ªå‘½ä»¤æ”¾åœ¨èŠ±æ‹¬å·ä¸­ã€‚
ä½œæ­¤é™åˆ¶çš„åŽŸå›&nbsp;æ˜¯ï¼Œå¦‚æžœä½&nbsp;æŠŠè¿™äº›å‘½ä»¤çš„å…¶ä¸­ä¸¤ä¸ªæ”¾åœ¨åŒä¸€ä¸ªå…¬å¼ä¸­ï¼Œ
\TeX\ å°†ä¸çŸ¥é“å¦‚ä½•åˆ’åˆ†å®ƒä»¬ã€‚

%The other commands are similar to |\over|, with the following exceptions:
%\ulist\compact
%\li |\atop| leaves out the fraction bar.
%\li |\above| provides a fraction bar of thickness \&lt;dimen&gt;.
%\li |\choose|
%leaves out the fraction bar and encloses the construct in parentheses.
%(It's called ``choose'' because $n \choose k$ is the notation for the
%number of ways of choosing $k$ things out of $n$ things.)
%\li |\brace| leaves out the fraction bar and encloses the construct in braces.
%\li |\brack|
%leaves out the fraction bar and encloses the construct in brackets.
%\endulist
%}%
%\example
%$${n+1 \over n-1}      \qquad {n+1 \atop n-1}   \qquad
%  {n+1 \above 2pt n-1} \qquad {n+1 \choose n-1} \qquad
%  {n+1 \brace n-1}     \qquad {n+1 \brack n-1}$$
%|
%\dproduces
%$${n+1 \over n-1}      \qquad {n+1 \atop n-1}   \qquad
%  {n+1 \above 2pt n-1} \qquad {n+1 \choose n-1} \qquad
%  {n+1 \brace n-1}     \qquad {n+1 \brack n-1}$$
%\endexample
%\enddesc
å…¶ä»–å‘½ä»¤ä¸Ž |\over| ç±»ä¼¼ï¼Œä½†æœ‰æ‰€ä¸åŒï¼š
\ulist\compact
\li |\atop| åŽ»æŽ‰åˆ†å¼çš„æ¨ªçº¿ã€‚
\li |\above| ç»™å‡ºåŽšåº¦ä¸º \&lt;dimen&gt; çš„åˆ†å¼æ¨ªçº¿ã€‚
\li |\choose| åŽ»æŽ‰åˆ†å¼æ¨ªçº¿ï¼Œå¹¶å°†ç»“æž„æ”¾åœ¨åœ†æ‹¬å·ä¸­ã€‚%
ï¼ˆç§°å®ƒä¸º``é€‰æ‹©''ï¼Œ
æ˜¯å›&nbsp;ä¸º $n \choose k$ è¡¨ç¤ºä»Ž $n$ ä¸ªä¸œè¥¿ä¸­ä»»å– $k$ ä¸ªçš„æ‰€æœ‰é€‰å–æ–¹å¼çš„æ•°ç›®ã€‚ï¼‰%
\li |\brace| åŽ»æŽ‰åˆ†å¼æ¨ªçº¿ï¼Œå¹¶å°†ç»“æž„æ”¾åœ¨èŠ±æ‹¬å·ä¸­ã€‚
\li |\brack| åŽ»æŽ‰åˆ†å¼æ¨ªçº¿ï¼Œå¹¶å°†ç»“æž„æ”¾åœ¨æ–¹æ‹¬å·ä¸­ã€‚
\endulist
}%
\example
$${n+1 \over n-1}      \qquad {n+1 \atop n-1}   \qquad
  {n+1 \above 2pt n-1} \qquad {n+1 \choose n-1} \qquad
  {n+1 \brace n-1}     \qquad {n+1 \brack n-1}$$
|
\dproduces
$${n+1 \over n-1}      \qquad {n+1 \atop n-1}   \qquad
  {n+1 \above 2pt n-1} \qquad {n+1 \choose n-1} \qquad
  {n+1 \brace n-1}     \qquad {n+1 \brack n-1}$$
\endexample
\enddesc

%\begindesc
%\cts overwithdelims {\&lt;delim$_1$&gt; \&lt;delim$_2$&gt;}
%\cts atopwithdelims {\&lt;delim$_1$&gt; \&lt;delim$_2$&gt;}
%\cts abovewithdelims {\&lt;delim$_1$&gt; \&lt;delim$_2$&gt; \&lt;dimen&gt;}
%\explain
%Each of these commands stacks one subformula on top of another one and
%surrounds the entire construct with \&lt;delim$_1$&gt; on the left and
%\&lt;delim$_2$&gt; on the right.  These commands follow the same rules as
%|\over|, |\atop|, and |\above|. The \&lt;dimen&gt; in |\abovewithdelims|
%specifies the thickness of the fraction bar.
%\example
%$${m \overwithdelims () n}\qquad
%  {m \atopwithdelims !|!| n}\qquad
%  {m \abovewithdelims \{\} 2pt n}$$
%|
%\dproduces
%$${m \overwithdelims () n}\qquad
%  {m \atopwithdelims || n}\qquad
%  {m \abovewithdelims \{\} 2pt n}$$
%\endexample
%\enddesc
\begindesc
\cts overwithdelims {\&lt;delim$_1$&gt; \&lt;delim$_2$&gt;}
\cts atopwithdelims {\&lt;delim$_1$&gt; \&lt;delim$_2$&gt;}
\cts abovewithdelims {\&lt;delim$_1$&gt; \&lt;delim$_2$&gt; \&lt;dimen&gt;}
\explain
è¿™é‡Œçš„æ¯ä¸ªå‘½ä»¤éƒ½å°†ä¸€ä¸ªå­å…¬å¼å&nbsp;†æ”¾åœ¨å¦ä¸€ä¸ªå­å…¬å¼ä¹‹ä¸Šï¼Œ
å¹¶å°†æ•´ä¸ªç»“æž„çš„å·¦è¾¹ç”¨ \&lt;delim$_1$&gt;ï¼Œå³è¾¹ç”¨ \&lt;delim$_2$&gt; åŒ…å›´ã€‚
è¿™äº›å‘½ä»¤éµå¾ªä¸Ž |\over|ã€|\atop| å’Œ |\above| ç›¸åŒçš„è§„åˆ™ã€‚
|\abovewithdelims| åŽé¢çš„ \&lt;dimen&gt; æŒ‡å®šåˆ†å¼æ¨ªçº¿çš„åŽšåº¦ã€‚
\example
$${m \overwithdelims () n}\qquad
  {m \atopwithdelims !|!| n}\qquad
  {m \abovewithdelims \{\} 2pt n}$$
|
\dproduces
$${m \overwithdelims () n}\qquad
  {m \atopwithdelims || n}\qquad
  {m \abovewithdelims \{\} 2pt n}$$
\endexample
\enddesc

%\begindesc
%\cts cases {}
%\explain
%^^{combinations, notation for}
%This command produces the mathematical form that denotes a choice among
%several cases.
%Each case has two parts, separated by `|&amp;|'.
%\TeX\ treats the first part as a math formula
%and the second part as ordinary text.  Each
%case must be followed by |\cr|.
\begindesc
\cts cases {}
\explain
^^{ç»„åˆæ•°è®°æ³•}
æ­¤å‘½ä»¤æŽ’å°ä¸€ä¸ªè¡¨ç¤ºä»Žå¤šä¸ªæƒ…å½¢ä¸­é€‰æ‹©çš„æ•°å­¦å½¢å¼ã€‚
æ¯ç§æƒ…å½¢ç”±ä¸¤éƒ¨åˆ†ç»„æˆï¼Œä¸¤è€…ä»¥ `|&amp;|' åˆ†éš”ã€‚
\TeX\ å°†ç¬¬ä¸€éƒ¨åˆ†è§†ä¸ºæ•°å­¦å…¬å¼ï¼Œç¬¬äºŒéƒ¨åˆ†è§†ä¸ºæ™®é€šæ–‡æœ¬ã€‚
æ¯ä¸ªæƒ…å½¢ä¹‹åŽå¿…é¡»åŠ&nbsp;ä¸Š |\cr|ã€‚

%\example
%$$g(x,y) = \cases{f(x,y),&amp;if $x&lt;y$\cr
%                  f(y,x),&amp;if $x&gt;y$\cr
%                  0,&amp;otherwise.\cr}$$
%|
%\dproduces
%$$g(x,y) = \cases{f(x,y),&amp;if $x&lt;y$\cr
%                  f(y,x),&amp;if $x&gt;y$\cr
%                  0,&amp;otherwise.\cr}$$
%\endexample
%\enddesc
\example
$$g(x,y) = \cases{f(x,y),&amp;if $x&lt;y$\cr
                  f(y,x),&amp;if $x&gt;y$\cr
                  0,&amp;otherwise.\cr}$$
|
\dproduces
$$g(x,y) = \cases{f(x,y),&amp;if $x&lt;y$\cr
                  f(y,x),&amp;if $x&gt;y$\cr
                  0,&amp;otherwise.\cr}$$
\endexample
\enddesc

%\begindesc
%\cts underbrace {\&lt;argument&gt;}
%\cts overbrace {\&lt;argument&gt;}
%\cts underline {\&lt;argument&gt;}
%\cts overline {\&lt;argument&gt;}
%\cts overleftarrow {\&lt;argument&gt;}
%\cts overrightarrow {\&lt;argument&gt;}
%\explain
%These commands place extensible ^{braces}, lines, or ^{arrows}
%over or under the subformula given by \&lt;argument&gt;.
%\TeX\ will make these constructs as wide as they need to be for
%the context.
%When \TeX\ produces the extended braces, lines, or arrows, it considers
%only the dimensions of the \minref{box} containing \&lt;argument&gt;.
%If you use more than one of these commands in a single formula, the
%braces, lines, or arrows they produce
%may not line up properly with each other.
%You can use the |\mathstrut| command (\xref \mathstrut)
%to overcome this difficulty.
%\example
%$$\displaylines{
%\underbrace{x \circ y}\qquad \overbrace{x \circ y}\qquad
%\underline{x \circ y}\qquad \overline{x \circ y}\qquad
%\overleftarrow{x \circ y}\qquad
%\overrightarrow{x \circ y}\cr
%{\overline r + \overline t}\qquad
%{\overline {r \mathstrut} + \overline {t \mathstrut}}\cr
%}$$
%|
%\dproduces
%$$\displaylines{
%\underbrace{x \circ y}\qquad \overbrace{x \circ y}\qquad
%\underline{x \circ y}\qquad \overline{x \circ y}\qquad
%\overleftarrow{x \circ y}\qquad
%\overrightarrow{x \circ y}\cr
%{\overline r + \overline t}\qquad
%{\overline {r \mathstrut} + \overline {t \mathstrut}}\cr
%}$$
%\endexample
%\enddesc
\begindesc
\cts underbrace {\&lt;argument&gt;}
\cts overbrace {\&lt;argument&gt;}
\cts underline {\&lt;argument&gt;}
\cts overline {\&lt;argument&gt;}
\cts overleftarrow {\&lt;argument&gt;}
\cts overrightarrow {\&lt;argument&gt;}
\explain
è¿™äº›å‘½ä»¤å°†å¯ä¼¸é•¿çš„^{èŠ±æ‹¬å·}ã€æ¨ªçº¿æˆ–^{ç®­å¤´}%
æ”¾åœ¨ç”± \&lt;argument&gt; ç»™å‡ºçš„å­å…¬å¼çš„ä¸Šè¾¹æˆ–ä¸‹è¾¹ã€‚
\TeX\ å°†è®©è¿™äº›ç»“æž„è¶³å¤Ÿå®½ä»¥é€‚åº”å†…å®¹ã€‚
å½“ \TeX\ æŽ’å°å¯ä¼¸é•¿çš„èŠ±æ‹¬å·ã€æ¨ªçº¿æˆ–ç®­å¤´æ—¶ï¼Œ
å®ƒåªè€ƒè™‘åŒ…å« \&lt;argument&gt; çš„ \minref{ç›’å­}çš„å°ºå¯¸ã€‚
å¦‚æžœä½&nbsp;åœ¨ä¸€ä¸ªå…¬å¼ä¸­ä½¿ç”¨è¿™äº›å‘½ä»¤ä¸­çš„ä¸¤ä¸ªä»¥ä¸Šï¼Œ
å…¶ä¸­æŽ’å°çš„èŠ±æ‹¬å·ã€æ¨ªçº¿æˆ–ç®­å¤´ä¹‹é—´å¯èƒ½æ—&nbsp;æ³•æ°å½“åœ°å¯¹é½ã€‚
ä½&nbsp;å¯ä»¥ä½¿ç”¨ |\mathstrut| å‘½ä»¤ï¼ˆ\xref\mathstrut ï¼‰å…‹æœæ­¤å›°éš¾ã€‚
\example
$$\displaylines{
\underbrace{x \circ y}\qquad \overbrace{x \circ y}\qquad
\underline{x \circ y}\qquad \overline{x \circ y}\qquad
\overleftarrow{x \circ y}\qquad
\overrightarrow{x \circ y}\cr
{\overline r + \overline t}\qquad
{\overline {r \mathstrut} + \overline {t \mathstrut}}\cr
}$$
|
\dproduces
$$\displaylines{
\underbrace{x \circ y}\qquad \overbrace{x \circ y}\qquad
\underline{x \circ y}\qquad \overline{x \circ y}\qquad
\overleftarrow{x \circ y}\qquad
\overrightarrow{x \circ y}\cr
{\overline r + \overline t}\qquad
{\overline {r \mathstrut} + \overline {t \mathstrut}}\cr
}$$
\endexample
\enddesc

%\begindesc\secondprinting{\vglue-.5\baselineskip\vskip0pt}
%\cts buildrel {\&lt;formula&gt; {\bt \\over} \&lt;relation&gt;}
%\explain
%^^{relations//putting formulas above}
%This command produces a \minref{box} in which \&lt;formula&gt;
%is placed on top of \&lt;relation&gt;. \TeX\ treats the result as a relation
%for spacing purposes \seeconcept{class}.
%\example
%$\buildrel \rm def \over \equiv$
%|
%\produces
%$\buildrel \rm def \over \equiv$
\begindesc%\secondprinting{\vglue-.5\baselineskip\vskip0pt}
\cts buildrel {\&lt;formula&gt; {\bt \\over} \&lt;relation&gt;}
\explain
^^{å…³ç³»ç¬¦//å°†å…¬å¼æ”¾åœ¨å…¶ä¸Š}
æ­¤å‘½ä»¤å°† \&lt;formula&gt; æ‰€åœ¨çš„\minref{ç›’å­}æ”¾åœ¨ \&lt;relation&gt; ä¸Šè¾¹ã€‚
\TeX\ å¤„ç†é—´éš”æ—¶å°†ç»“æžœè§†ä¸ºä¸€ä¸ªå…³ç³»ç¬¦\seeconcept{ç±»}ã€‚
\example
$\buildrel \rm def \over \equiv$
|
\produces
$\buildrel \rm def \over \equiv$

%\eix^^{fractions}
%\eix^^{stacking subformulas}
%\endexample
%\enddesc
\eix^^{åˆ†å¼}
\eix^^{å&nbsp;†å&nbsp;å­å…¬å¼}
\endexample
\enddesc

%\secondprinting{\vfill\eject}


%==========================================================================
%\subsection {Dots}
\subsection {åœ†ç‚¹}

%\begindesc
%\bix^^{dots}
%\easy\cts ldots {}
%\cts cdots {}
%\explain
%These commands produce three ^{dots} in a row.  For |\ldots|, the dots
%are on the baseline; for |\cdots|, the dots are centered with respect to
%the axis (see the explanation of |\vcenter|, \xref\vcenter).
\begindesc
\bix^^{åœ†ç‚¹}
\easy\cts ldots {}
\cts cdots {}
\explain
è¿™ä¸¤ä¸ªå‘½ä»¤éƒ½æŽ’å°ä¸‰ä¸ªä¸€æŽ’çš„^{åœ†ç‚¹}ã€‚å¯¹äºŽ |\ldots|ï¼Œ
åœ†ç‚¹æ”¾åœ¨åŸºçº¿ä¸Šï¼›å¯¹äºŽ |\cdots|ï¼Œåœ†ç‚¹æ”¾åœ¨ä¸­è½´çº¿ä¸Š%
ï¼ˆè§ \xref\vcenter å¯¹ |\vcenter| çš„è§£é‡Šï¼‰ã€‚

%\example
%$t_1 + t_2 + \cdots + t_n \qquad x_1,x_2, \ldots\,, x_r$
%|
%\produces
%$t_1 + t_2 + \cdots + t_n \qquad x_1,x_2, \ldots\,, x_r$
%\endexample
%\enddesc
\example
$t_1 + t_2 + \cdots + t_n \qquad x_1,x_2, \ldots\,, x_r$
|
\produces
$t_1 + t_2 + \cdots + t_n \qquad x_1,x_2, \ldots\,, x_r$
\endexample
\enddesc

%\begindesc
%\easy\cts vdots {}
%\explain
%This command produces three vertical dots.
%\example
%$$\eqalign{f(\alpha_1)&amp; = f(\beta_1)\cr
%   \noalign{\kern -4pt}%
%   &amp;\phantom{a}\vdots\cr % moves the dots right a bit
%   f(\alpha_k)&amp; = f(\beta_k)\cr}$$
%|
%\dproduces
%$$\eqalign{f(\alpha_1)&amp; = f(\beta_1)\cr
%   \noalign{\kern -4pt}%
%   &amp;\phantom{a}\vdots\cr
%   f(\alpha_k)&amp; = f(\beta_k)\cr}$$
%\endexample
%\enddesc
\begindesc
\easy\cts vdots {}
\explain
æ­¤å‘½ä»¤æŽ’å°ä¸‰ä¸ªç«–ç›´çš„åœ†ç‚¹ã€‚
\example
$$\eqalign{f(\alpha_1)&amp; = f(\beta_1)\cr
   \noalign{\kern -4pt}%
   &amp;\phantom{a}\vdots\cr % moves the dots right a bit
   f(\alpha_k)&amp; = f(\beta_k)\cr}$$
|
\dproduces
$$\eqalign{f(\alpha_1)&amp; = f(\beta_1)\cr
   \noalign{\kern -4pt}%
   &amp;\phantom{a}\vdots\cr
   f(\alpha_k)&amp; = f(\beta_k)\cr}$$
\endexample
\enddesc

%\begindesc
%\cts ddots {}
%\explain
%This command produces three dots on a diagonal.
%Its most common use is to indicate repetition along the diagonal of a matrix.
%\example
%$$\pmatrix{0&amp;\ldots&amp;0\cr
%           \vdots&amp;\ddots&amp;\vdots\cr
%           0&amp;\ldots&amp;0\cr}$$
%|
%\dproduces
%$$\pmatrix{0&amp;\ldots&amp;0\cr
%           \vdots&amp;\ddots&amp;\vdots\cr
%           0&amp;\ldots&amp;0\cr}$$
\begindesc
\cts ddots {}
\explain
æ­¤å‘½ä»¤æŽ’å°æ–œçº¿ä¸Šçš„ä¸‰ä¸ªåœ†ç‚¹ã€‚å®ƒå¸¸ç”¨äºŽè¡¨ç¤ºæ²¿çŸ©é˜µå¯¹è§’çº¿çš„é‡å¤ã€‚
\example
$$\pmatrix{0&amp;\ldots&amp;0\cr
           \vdots&amp;\ddots&amp;\vdots\cr
           0&amp;\ldots&amp;0\cr}$$
|
\dproduces
$$\pmatrix{0&amp;\ldots&amp;0\cr
           \vdots&amp;\ddots&amp;\vdots\cr
           0&amp;\ldots&amp;0\cr}$$

%\eix^^{dots}
%\endexample
%\enddesc
\eix^^{åœ†ç‚¹}
\endexample
\enddesc

%\see |\dots| \ctsref\dots.
\see |\dots|\ctsref\dots ã€‚

%==========================================================================
%\subsection {Delimiters}
\subsection {å®šç•Œç¬¦}

%\begindesc
%\bix^^{delimiters}
%%
%\cts lgroup {}
%\cts rgroup {}
%\explain
%These commands produce large left and right ^{parentheses}
%that are defined as opening and closing \minref{delimiter}s.
%The smallest available size for these delimiters is |\Big|.
%If you use smaller sizes, you'll get weird characters.
%\example
%$$\lgroup\dots\rgroup\qquad\bigg\lgroup\dots\bigg\rgroup$$
%|
%\dproduces
%$$\lgroup\dots\rgroup\qquad\bigg\lgroup\dots\bigg\rgroup$$
%\endexample
%\enddesc
\begindesc
\bix^^{å®šç•Œç¬¦}
%
\cts lgroup {}
\cts rgroup {}
\explain
è¿™ä¸¤ä¸ªå‘½ä»¤æŽ’å°å¤§å·çš„å·¦å’Œå³^{åœ†æ‹¬å·}ï¼Œ
å®ƒä»¬åˆ†åˆ«ä½œä¸ºå¼€å®šç•Œç¬¦å’Œé—­\minref{å®šç•Œç¬¦}ã€‚
è¿™ä¸¤ä¸ªå®šç•Œç¬¦çš„æœ€å°å¯ç”¨å°ºå¯¸ä¸º |\Big|ã€‚
å¦‚æžœä½¿ç”¨æ›´å°çš„å°ºå¯¸ï¼Œä½&nbsp;å°†å¾—åˆ°å¥‡æ€ªçš„å­—ç¬¦ã€‚
\example
$$\lgroup\dots\rgroup\qquad\bigg\lgroup\dots\bigg\rgroup$$
|
\dproduces
$$\lgroup\dots\rgroup\qquad\bigg\lgroup\dots\bigg\rgroup$$
\endexample
\enddesc

%\begindesc
%\margin{{\tt\\vert} and {\tt\\Vert} were explained elsewhere.}
%\easy\cts left {}
%\cts right {}
%\explain
%These commands must be used together in the pattern:
%\display
%{{\bt \\left} \&lt;delim$_1$&gt; \&lt;subformula&gt; {\bt \\right} \&lt;delim$_2$&gt;}
%This construct causes \TeX\ to produce \&lt;subformula&gt;,
%enclosed in the \minref{delimiter}s \&lt;delim$_1$&gt; and \&lt;delim$_2$&gt;.
%The vertical size of the delimiter is adjusted to fit the
%vertical size (height plus depth) of \&lt;subformula&gt;.  \&lt;delim$_1$&gt; and
%\&lt;delim$_2$&gt; need not correspond.
%For instance, you could use `|]|' as a left delimiter
%and `|(|' as a right delimiter in a single use of |\left|
%and |\right|.
\begindesc
\margin{{\tt\\vert} and {\tt\\Vert} were explained elsewhere.}
\easy\cts left {}
\cts right {}
\explain
è¿™ä¸¤ä¸ªå‘½ä»¤å¿…é¡»æŒ‰ç…§ä¸‹é¢æ¨¡å¼ä¸€èµ·ä½¿ç”¨ï¼š
\display
{{\bt \\left} \&lt;delim$_1$&gt; \&lt;subformula&gt; {\bt \\right} \&lt;delim$_2$&gt;}
è¿™ä¸ªæž„é€&nbsp;å°†è®© \TeX\ æŽ’å° \&lt;subformula&gt;ï¼Œ
å¹¶ç”¨\minref{å®šç•Œç¬¦} \&lt;delim$_1$&gt; å’Œ \&lt;delim$_2$&gt; åŒ…å›´å®ƒã€‚
\TeX\ è°ƒæ•´å®šç•Œç¬¦çš„ç«–ç›´å°ºå¯¸ä»¥é€‚åº” \&lt;subformula&gt; çš„ç«–ç›´å°ºå¯¸ï¼ˆé«˜åº¦åŠ&nbsp;æ·±åº¦ï¼‰ã€‚
\&lt;delim$_1$&gt; å’Œ \&lt;delim$_2$&gt; ä¸éœ€è¦ç›¸å¯¹åº”ã€‚
ä¸¾ä¸ªä¾‹å­ï¼Œåœ¨ä½¿ç”¨ |\left| å’Œ |\right| æ—¶ï¼Œ
ä½&nbsp;å¯ä»¥å°† `|]|' ä½œä¸ºå·¦å®šç•Œç¬¦ï¼Œè€Œå°† `|(|' ä½œä¸ºå³å®šç•Œç¬¦ã€‚

%|\left| and |\right| have the important property that they define a
%group, i.e., they act like left and right braces.  This grouping
%property is particularly useful when you put ^|\over| (\xref{\over}) or
%a related command between |\left| and |\right|, since you don't need to
%put braces around the fraction constructed by |\over|.
|\left| å’Œ |\right| æœ‰ä¸ªé‡è¦æ€§è´¨æ˜¯å®ƒä»¬å®šä¹‰äº†ä¸€ä¸ªç¼–ç»„ï¼Œ
å³å®ƒä»¬èƒ½å¤Ÿå……å½“å·¦å’Œå³èŠ±æ‹¬å·ã€‚
å½“ä½&nbsp;åœ¨|\left| å’Œ |\right| ä¹‹é—´æ”¾ä¸Š ^|\over|ï¼ˆ\xref{\over}ï¼‰æˆ–å…¶ä»–ç›¸å…³å‘½ä»¤æ—¶ï¼Œ
æ­¤ç¼–ç»„æ€§è´¨å°±å¾ˆæœ‰ç”¨ï¼Œå›&nbsp;ä¸ºä½&nbsp;æ—&nbsp;éœ€åœ¨ |\over| æž„é€&nbsp;çš„åˆ†å¼ä¸¤è¾¹åŠ&nbsp;ä¸ŠèŠ±æ‹¬å·ã€‚

%If you want a left delimiter but not a right delimiter, you can use `|.|' in
%place of the delimiter you don't want and it will turn into empty space
%(of width ^|\nulldelimiterspace|).
%\example
%$$\left\Vert\matrix{a&amp;b\cr c&amp;d\cr}\right\Vert
%  \qquad \left\uparrow q_1\atop q_2\right.$$
%|
%\dproduces
%$$\left\Vert\matrix{a&amp;b\cr c&amp;d\cr}\right\Vert
%  \qquad \left\uparrow q_1\atop q_2\right.$$
%\endexample
%\enddesc
å¦‚æžœä½&nbsp;éœ€è¦å·¦å®šç•Œç¬¦ä½†ä¸éœ€è¦å³å®šç•Œç¬¦ï¼Œ
ä½&nbsp;å¯ä»¥ç”¨ `|.|' ä»£æ›¿ä½&nbsp;ä¸éœ€è¦çš„å®šç•Œç¬¦ï¼Œ
è¿™æ&nbsp;·å®ƒå°±å˜æˆä¸€ä¸ªç©ºç™½ï¼ˆå®½åº¦ä¸º ^|\nulldelimiterspace|ï¼‰ã€‚
\example
$$\left\Vert\matrix{a&amp;b\cr c&amp;d\cr}\right\Vert
  \qquad \left\uparrow q_1\atop q_2\right.$$
|
\dproduces
$$\left\Vert\matrix{a&amp;b\cr c&amp;d\cr}\right\Vert
  \qquad \left\uparrow q_1\atop q_2\right.$$
\endexample
\enddesc

%\begindesc
%\cts delimiter {\&lt;number&gt;}
%\explain
%This command produces a delimiter whose characteristics are given by
%\&lt;number&gt;.  \&lt;number&gt; is normally written in hexadecimal notation.
%You can use the |\delimiter| command instead of a character in any context
%where \TeX\ expects a delimiter (although the command is rarely used
%outside of a macro definition).
%Suppose that \&lt;number&gt; is the hexadecimal number $cs_1s_2s_3
%l_1l_2l_3$.  Then \TeX\ takes the delimiter to have
%\minref{class} $c$, small variant
%$s_1s_2s_3$, and large variant $l_1l_2l_3$.  Here $s_1s_2s_3$ indicates
%the math character found in position $s_2s_3$ of family $s_1$, and
%similarly for $l_1l_2l_3$.  This is the same convention as the one
%used for ^|\mathcode| (\xref\mathcode).
%\example
%\def\vert{\delimiter "026A30C} % As in plain TeX.
%|
%\endexample
%\enddesc
\begindesc
\cts delimiter {\&lt;number&gt;}
\explain
æ­¤å‘½ä»¤æŽ’å°ç”¨ \&lt;number&gt; åˆ»ç”»å…¶ç‰¹æ€§çš„å®šç•Œç¬¦ã€‚\&lt;number&gt; é€šå¸¸ç”¨åå…­è¿›åˆ¶è¡¨ç¤ºã€‚
åœ¨ \TeX\ éœ€è¦å®šç•Œç¬¦çš„ä»»ä½•åœ°æ–¹ä½&nbsp;éƒ½å¯ä»¥ç”¨ |\delimiter| å‘½ä»¤ä»£æ›¿ä¸€ä¸ªå­—ç¬¦%
ï¼ˆå°½ç®¡æ­¤å‘½ä»¤å¾ˆå°‘åœ¨å®å®šä¹‰ä¹‹å¤–çš„åœ°æ–¹ä½¿ç”¨ï¼‰ã€‚
å‡è®¾ \&lt;number&gt; ä¸ºåå…­è¿›åˆ¶æ•° $cs_1s_2s_3l_1l_2l_3$ã€‚
åˆ™ \TeX\ çŸ¥é“è¯¥å®šç•Œç¬¦å±žäºŽç¬¬$c$\minref{ç±»}ï¼Œ
å°å·å˜ä½“ä¸º $s_1s_2s_3$, è€Œå¤§å·å˜ä½“ä¸º $l_1l_2l_3$ã€‚
è¿™é‡Œ $s_1s_2s_3$ è¡¨ç¤ºç¬¬ $s_1$ æ—ä½ç½® $s_2s_3$ çš„æ•°å­¦å­—ç¬¦ï¼Œ
$l_1l_2l_3$ ç±»ä¼¼ã€‚è¿™é‡Œä½¿ç”¨ä¸Ž ^|\mathcode|ï¼ˆ\xref\mathcode ï¼‰ä¸€æ&nbsp;·çš„çº¦å®šã€‚
\example
\def\vert{\delimiter "026A30C} % As in plain TeX.
|
\endexample
\enddesc

%\begindesc
%\margin{{\tt\\delcode} was explained in two places.  The
%combined explanation is now in `General operations'.}
%\cts delimiterfactor {\param{number}}
%\cts delimitershortfall {\param{number}}
%\explain
%^^{delimiters//height of}
%These parameters together tell \TeX\ how the height of a \minref{delimiter}
%should be related to the vertical size of the subformula
%with which the delimiter is associated.
%|\delimiterfactor| gives the minimum
%ratio of the delimiter size to the vertical size of the subformula, and
%|\delimitershortfall| gives the maximum by which the height of the
%delimiter will be reduced from that of the vertical size of the subformula.
\begindesc
\margin{{\tt\\delcode} was explained in two places.  The
combined explanation is now in `General operations'.}
\cts delimiterfactor {\param{number}}
\cts delimitershortfall {\param{number}}
\explain
^^{å®šç•Œç¬¦//å®šç•Œç¬¦é«˜åº¦}
è¿™ä¸¤ä¸ªå‚æ•°å…±åŒç¡®å®šäº†\minref{å®šç•Œç¬¦}é«˜åº¦ä¸Žå…¶ä¸­å­å…¬å¼çš„ç«–ç›´å°ºå¯¸çš„å…³ç³»ã€‚
|\delimiterfactor| ç»™å‡ºå®šç•Œç¬¦é«˜åº¦ç›¸å¯¹å­å…¬å¼ç«–ç›´å°ºå¯¸çš„æœ€å°æ¯”ä¾‹ï¼Œ
è€Œ |\delimitershortfall| ç»™å‡ºå®šç•Œç¬¦é«˜åº¦ç›¸å¯¹å­å…¬å¼ç«–ç›´å°ºå¯¸çš„æœ€å¤§å·®è·ã€‚

%Suppose that the \minref{box} containing the subformula
%has height $h$ and depth $d$, and let $y=2\,\max(h,d)$.
%Let the value of |\delimiterfactor| be $f$ and the value of
%|\delimitershortfall| be $\delta$.
%Then \TeX\ takes the minimum delimiter size to be at least $y \cdot
%f/1000$ and at least $y-\delta$.  In particular, if |\delimiterfactor|
%is exactly $1000$ then \TeX\ will try to make a delimiter at least as tall
%as the formula to which it is attached.
%See \knuth{page~152 and page~446 (Rule 19)}
%for the exact details of how \TeX\ uses these parameters.
%\PlainTeX\ sets |\delimiter!-factor| to $901$ and
%|\delimiter!-shortfall| to |5pt|.
%\enddesc
å‡è®¾åŒ…å«å­å…¬å¼çš„\minref{ç›’å­}çš„é«˜åº¦ä¸º $h$ æ·±åº¦ä¸º $d$ï¼Œ
ä¸”ä»¤ $y=2\,\max(h,d)$ã€‚
è®¾ |\delimiterfactor| çš„å€¼ä¸º $f$ï¼Œ|\delimitershortfall| çš„å€¼ä¸º $\delta$ã€‚
åˆ™ \TeX\ é€‰å–çš„å®šç•Œç¬¦é«˜åº¦è‡³å°‘ä¸º $y \cdot f/1000$ï¼Œä¸”è‡³å°‘ä¸º $y-\delta$ã€‚
ç‰¹åˆ«åœ°ï¼Œå¦‚æžœ |\delimiterfactor| æ°å¥½ä¸º $1000$ï¼Œ
åˆ™ \TeX\ å°†è¯•ç€ç”Ÿæˆä¸€ä¸ªè‡³å°‘å’Œå…¶ä¸­çš„å­å…¬å¼ä¸€æ&nbsp;·é«˜çš„å®šç•Œç¬¦ã€‚
è§\knuth{ç¬¬~152~é¡µå’Œç¬¬~446~é¡µï¼ˆè§„åˆ™19ï¼‰}ä¸­ \TeX\ å¦‚ä½•ä½¿ç”¨è¿™äº›å‚æ•°çš„ç»†èŠ‚ã€‚
\PlainTeX\ è®¾å®š |\delimiter!-factor| ä¸º $901$ï¼Œ
|\delimiter!-shortfall| ä¸º |5pt|ã€‚
\enddesc

%\see |\delcode| (\xref\delcode), |\vert|, |\Vert|,
%and |\backslash| (\xref\vert).
%\eix^^{delimiters}
\see |\delcode|ï¼ˆ\xref\delcode )ã€|\vert|ã€|\Vert| å’Œ |\backslash|ï¼ˆ\xref\vert ï¼‰ã€‚
\eix^^{å®šç•Œç¬¦}

%==========================================================================
%\subsection {Matrices}
\subsection {çŸ©é˜µ}

%\begindesc
%\cts matrix
%   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
%\cts pmatrix
%   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
%\cts bordermatrix
%   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
%\explain
%Each of these three commands produces a ^{matrix}.
%The elements of each row of the input matrix
%are separated by `|&amp;|' and each row in turn is ended
%by |\cr|.
%(This is the same form that is used for an
%\minref{alignment}.)
%The commands differ in the following ways:
%\ulist\compact
%\li |\matrix| produces a matrix without any surrounding or inserted
%\minref{delimiter}s.
%\li |\pmatrix| produces a matrix surrounded by parentheses.
%\li |\bordermatrix| produces a matrix in which the first row and the first
%column are treated as labels.  (The first element of the first row is
%usually left blank.)  The rest of the matrix is enclosed in
%parentheses.
%\endulist
%\TeX\ can make the parentheses for |\pmatrix| and |\bordermatrix| as large as
%they need to be by inserting vertical extensions.  If you want a matrix
%to be surrounded by delimiters other than parentheses, you should use
%|\matrix| in conjunction with |\left| and |\right| (\xref \left).
\begindesc
\cts matrix
   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
\cts pmatrix
   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
\cts bordermatrix
   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
\explain
è¿™ä¸‰ä¸ªå‘½ä»¤æ¯ä¸ªéƒ½æŽ’å°ä¸€ä¸ª^{çŸ©é˜µ}ï¼Œ
è¾“å…¥çŸ©é˜µæ—¶å„è¡Œçš„å…ƒç´&nbsp;ä¹‹é—´ç”¨ `|&amp;|' åˆ†éš”ï¼Œè€Œå„è¡Œç”¨ |\cr| ç»“å°¾ã€‚%
ï¼ˆè¿™é‡Œä½¿ç”¨ä¸Ž\minref{é˜µåˆ—}ä¸€æ&nbsp;·çš„å½¢å¼ã€‚ï¼‰%
è¿™äº›å‘½ä»¤ä¹‹é—´çš„åŒºåˆ«å¦‚ä¸‹ï¼š
\ulist\compact
\li |\matrix| æŽ’å°ä¸€ä¸ªå››å‘¨ç©ºç™½ä¸å¸¦\minref{å®šç•Œç¬¦}çš„çŸ©é˜µã€‚
\li |\pmatrix| æŽ’å°ä¸€ä¸ªä¸¤è¾¹å¸¦åœ†æ‹¬å·çš„çŸ©é˜µã€‚
\li |\bordermatrix| æŽ’å°ä¸€ä¸ªå°†ç¬¬ä¸€è¡Œå’Œç¬¬ä¸€åˆ—è§†ä¸ºæ&nbsp;‡å·çš„çŸ©é˜µã€‚%
ï¼ˆç¬¬ä¸€è¡Œçš„ç¬¬ä¸€ä¸ªå…ƒç´&nbsp;é€šå¸¸ä¸ºç©ºç™½ã€‚ï¼‰%
çŸ©é˜µçš„å…¶ä»–å…ƒç´&nbsp;è¢«åœ†æ‹¬å·åŒ…å«ã€‚
\endulist
é€šè¿‡å¢žåŠ&nbsp;ç«–ç›´å»¶ä¼¸ï¼Œ\TeX\ èƒ½å¤Ÿä¸º |\pmatrix| å’Œ |\bordermatrix| åˆ¶ä½œè¶³å¤Ÿå¤§çš„åœ†æ‹¬å·ã€‚
å¦‚æžœä½&nbsp;éœ€è¦ç”¨ä¸åŒäºŽåœ†æ‹¬å·çš„å®šç•Œç¬¦åŒ…å›´çŸ©é˜µï¼Œä½&nbsp;åº”å½“å°†
|\matrix| ä¸Ž |\left| å’Œ |\right|ï¼ˆ\xref\left ï¼‰åˆèµ·æ¥ä½¿ç”¨ã€‚

%\example
%$$\displaylines{
%   \matrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
%           t_{21}&amp;t_{22}&amp;t_{23}\cr
%           t_{31}&amp;t_{32}&amp;t_{33}\cr}\qquad
%\left\{\matrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
%           t_{21}&amp;t_{22}&amp;t_{23}\cr
%           t_{31}&amp;t_{32}&amp;t_{33}\cr}\right\}\cr
%\pmatrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
%           t_{21}&amp;t_{22}&amp;t_{23}\cr
%           t_{31}&amp;t_{32}&amp;t_{33}\cr}\qquad
%\bordermatrix{&amp;c_1&amp;c_2&amp;c_3\cr
%           r_1&amp;t_{11}&amp;t_{12}&amp;t_{13}\cr
%           r_2&amp;t_{21}&amp;t_{22}&amp;t_{23}\cr
%           r_3&amp;t_{31}&amp;t_{32}&amp;t_{33}\cr}\cr}$$
%|
%\dproduces
%$$\displaylines{
%   \matrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
%   t_{21}&amp;t_{22}&amp;t_{23}\cr
%   t_{31}&amp;t_{32}&amp;t_{33}\cr}\qquad
%\left\{\matrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
%   t_{21}&amp;t_{22}&amp;t_{23}\cr
%   t_{31}&amp;t_{32}&amp;t_{33}\cr}\right\}\cr
%\pmatrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
%   t_{21}&amp;t_{22}&amp;t_{23}\cr
%   t_{31}&amp;t_{32}&amp;t_{33}\cr}\qquad
%\bordermatrix{&amp;c_1&amp;c_2&amp;c_3\cr
%   r_1&amp;t_{11}&amp;t_{12}&amp;t_{13}\cr
%   r_2&amp;t_{21}&amp;t_{22}&amp;t_{23}\cr
%   r_3&amp;t_{31}&amp;t_{32}&amp;t_{33}\cr}\cr}$$
%\endexample
%\enddesc
\example
$$\displaylines{
   \matrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
           t_{21}&amp;t_{22}&amp;t_{23}\cr
           t_{31}&amp;t_{32}&amp;t_{33}\cr}\qquad
\left\{\matrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
           t_{21}&amp;t_{22}&amp;t_{23}\cr
           t_{31}&amp;t_{32}&amp;t_{33}\cr}\right\}\cr
\pmatrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
           t_{21}&amp;t_{22}&amp;t_{23}\cr
           t_{31}&amp;t_{32}&amp;t_{33}\cr}\qquad
\bordermatrix{&amp;c_1&amp;c_2&amp;c_3\cr
           r_1&amp;t_{11}&amp;t_{12}&amp;t_{13}\cr
           r_2&amp;t_{21}&amp;t_{22}&amp;t_{23}\cr
           r_3&amp;t_{31}&amp;t_{32}&amp;t_{33}\cr}\cr}$$
|
\dproduces
$$\displaylines{
   \matrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
   t_{21}&amp;t_{22}&amp;t_{23}\cr
   t_{31}&amp;t_{32}&amp;t_{33}\cr}\qquad
\left\{\matrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
   t_{21}&amp;t_{22}&amp;t_{23}\cr
   t_{31}&amp;t_{32}&amp;t_{33}\cr}\right\}\cr
\pmatrix{t_{11}&amp;t_{12}&amp;t_{13}\cr
   t_{21}&amp;t_{22}&amp;t_{23}\cr
   t_{31}&amp;t_{32}&amp;t_{33}\cr}\qquad
\bordermatrix{&amp;c_1&amp;c_2&amp;c_3\cr
   r_1&amp;t_{11}&amp;t_{12}&amp;t_{13}\cr
   r_2&amp;t_{21}&amp;t_{22}&amp;t_{23}\cr
   r_3&amp;t_{31}&amp;t_{32}&amp;t_{33}\cr}\cr}$$
\endexample
\enddesc

%==========================================================================
%\subsection {Roots and radicals}
\subsection {æ&nbsp;¹å·ä¸Žæ&nbsp;¹æ•°}

%\begindesc
%\easy\cts sqrt {\&lt;argument&gt;}
%\explain
%This command produces the notation for the square root of \&lt;argument&gt;.
%\example
%$$x = {-b\pm\sqrt{b^2-4ac} \over 2a}$$
%|
%\dproduces
%$$x = {-b\pm\sqrt{b^2-4ac} \over 2a}$$
%\endexample
%\enddesc
\begindesc
\easy\cts sqrt {\&lt;argument&gt;}
\explain
æ­¤å‘½ä»¤æŽ’å° \&lt;argument&gt; çš„å¹³æ–¹æ&nbsp;¹ã€‚
\example
$$x = {-b\pm\sqrt{b^2-4ac} \over 2a}$$
|
\dproduces
$$x = {-b\pm\sqrt{b^2-4ac} \over 2a}$$
\endexample
\enddesc

%\begindesc
%\easy\cts root {\&lt;argument$_1$&gt; {\bt \\of} \&lt;argument$_2$&gt;}
%\explain
%This command produces the notation for a root of \&lt;argument$_2$&gt;, where the
%root is given by \&lt;argument$_1$&gt;.
%\example
%$\root \alpha \of {r \cos \theta}$
%|
%\produces
%$\root \alpha \of {r \cos \theta}$
%\endexample
%\enddesc
\begindesc
\easy\cts root {\&lt;argument$_1$&gt; {\bt \\of} \&lt;argument$_2$&gt;}
\explain
æ­¤å‘½ä»¤æŽ’å° \&lt;argument$_2$&gt; çš„ \&lt;argument$_1$&gt; æ¬¡æ&nbsp;¹å·ã€‚
\example
$\root \alpha \of {r \cos \theta}$
|
\produces
$\root \alpha \of {r \cos \theta}$
\endexample
\enddesc

%\begindesc
%\cts radical {\&lt;number&gt;}
%\explain
%This command produces a radical sign
%whose characteristics are given by
%\&lt;number&gt;.  It uses the same representation as the delimiter code
%^^{delimiter codes}
%in the ^|\delcode| command (\xref \delcode).
\begindesc
\cts radical {\&lt;number&gt;}
\explain
æ­¤å‘½ä»¤æŽ’å°ç”¨ \&lt;number&gt; åˆ»ç”»å…¶ç‰¹æ€§çš„æ&nbsp;¹æ•°ç¬¦å·ã€‚
å®ƒä½¿ç”¨çš„å®šç•Œç&nbsp;è¡¨ç¤ºæ³•ä¸Ž ^|\delcode| å‘½ä»¤ï¼ˆ\xref\delcode ï¼‰çš„ç›¸åŒã€‚
^^{å®šç•Œç&nbsp;}

%\example
%\def\sqrt{\radical "270370} % as in plain TeX
%|
%\endexample
%\enddesc
\example
\def\sqrt{\radical "270370} % as in plain TeX
|
\endexample
\enddesc


%==========================================================================
%\section {Equation numbers}
\section {æ–¹ç¨‹ç¼–å·}

%\begindesc
%\easy\cts eqno {}
%\cts leqno {}
%\explain
%These commands attach an equation number to a displayed formula.
%|\eqno| puts the equation number on the right and |\leqno| puts it on
%the left.
%The commands must be given at the end of the formula.
%If you have a multiline display and you want to number more than one
%of the lines, use the |\eq!-alignno| or |\leq!-alignno| command
%(\xref \eqalignno).
\begindesc
\easy\cts eqno {}
\cts leqno {}
\explain
è¿™ä¸¤ä¸ªå‘½ä»¤ç»™é™ˆåˆ—å…¬å¼åŠ&nbsp;ä¸Šæ–¹ç¨‹ç¼–å·ã€‚
|\eqno| å°†ç¼–å·æ”¾åœ¨å³ä¾§ï¼Œè€Œ|\leqno| å°†ç¼–å·æ”¾åœ¨å·¦ä¾§ã€‚
è¿™ä¸¤ä¸ªå‘½ä»¤å¿…é¡»æ”¾åœ¨å…¬å¼æœ«å°¾ã€‚
å¦‚æžœä½&nbsp;æœ‰ä¸ªå¤šè¡Œé™ˆåˆ—å…¬å¼ï¼Œè€Œä½&nbsp;å¸Œæœ›ç»™ä¸æ­¢ä¸€è¡Œç¼–å·ï¼Œ
ä½&nbsp;å¯ä»¥ç”¨ |\eq!-alignno| æˆ– |\leq!-alignno| å‘½ä»¤ï¼ˆ\xref\eqalignno ï¼‰ã€‚

%These commands are valid only in display math mode.
è¿™ä¸¤ä¸ªå‘½ä»¤åªèƒ½åœ¨é™ˆåˆ—æ•°å­¦æ¨¡å¼ä¸­ä½¿ç”¨ã€‚

%\example
%$$e^{i\theta} = \cos \theta + i \sin \theta\eqno{(11)}$$
%|
%\produces
%$$e^{i\theta} = \cos \theta + i \sin \theta\eqno{(11)}$$
%\endexample
%\example
%$$\cos^2 \theta + \sin^2 \theta = 1\leqno{(12)}$$
%|
%\produces
%\abovedisplayskip = -\baselineskip
%$$\cos^2 \theta + \sin^2 \theta = 1\leqno{(12)}$$
%\endexample
%\enddesc
\example
$$e^{i\theta} = \cos \theta + i \sin \theta\eqno{(11)}$$
|
\produces
$$e^{i\theta} = \cos \theta + i \sin \theta\eqno{(11)}$$
\endexample
\example
$$\cos^2 \theta + \sin^2 \theta = 1\leqno{(12)}$$
|
\produces
\abovedisplayskip = -\baselineskip
$$\cos^2 \theta + \sin^2 \theta = 1\leqno{(12)}$$
\endexample
\enddesc


%==========================================================================
%\section {Multiline displays}
\section {å¤šè¡Œé™ˆåˆ—å…¬å¼}

%\begindesc
%\bix^^{displays//multiline}
%\cts displaylines
%   {{\bt \rqbraces{\&lt;line&gt;\ths\\cr$\ldots$\&lt;line&gt;\ths\\cr}}}
%\explain
%This command produces a multiline math display in which each line is
%centered independently of the other lines.
%You can use the |\noalign| command (\xref \noalign) to change the amount
%of space between two lines of a multiline display.
\begindesc
\bix^^{é™ˆåˆ—å…¬å¼//å¤šè¡Œé™ˆåˆ—å…¬å¼}
\cts displaylines
   {{\bt \rqbraces{\&lt;line&gt;\ths\\cr$\ldots$\&lt;line&gt;\ths\\cr}}}
\explain
æ­¤å‘½ä»¤æŽ’å°ä¸€ä¸ªå¤šè¡Œé™ˆåˆ—å…¬å¼ï¼Œå…¶ä¸­çš„å„è¡Œç‹¬ç«‹åœ°å±…ä¸­æ”¾ç½®ã€‚
ä½&nbsp;å¯ä»¥ä½¿ç”¨ |\noalign| å‘½ä»¤ï¼ˆ\xref\noalign ï¼‰æ”¹å˜å¤šè¡Œé™ˆåˆ—å…¬å¼ä¸­ä¸¤è¡Œçš„é—´éš”ã€‚

%If you want to attach equation numbers to some or all of the equations
%in a multiline math display, you should use |\eqalignno| or
%|\leqalignno|.
%\example
%$$\displaylines{(x+a)^2 = x^2+2ax+a^2\cr
%                (x+a)(x-a) = x^2-a^2\cr}$$
%|
%\dproduces\centereddisplays
%$$\displaylines{
%(x+a)^2 = x^2+2ax+a^2\cr
%(x+a)(x-a) = x^2-a^2\cr
%}$$
%\endexample
%\enddesc
å¦‚æžœä½&nbsp;å¸Œæœ›ç»™å¤šè¡Œé™ˆåˆ—å…¬å¼çš„æŸä¸ªæˆ–æŸäº›æ–¹ç¨‹æ·»åŠ&nbsp;ç¼–å·ï¼Œ
ä½&nbsp;åº”å½“ä½¿ç”¨|\eqalignno| æˆ– |\leqalignno|ã€‚
\example
$$\displaylines{(x+a)^2 = x^2+2ax+a^2\cr
                (x+a)(x-a) = x^2-a^2\cr}$$
|
\dproduces\centereddisplays
$$\displaylines{
(x+a)^2 = x^2+2ax+a^2\cr
(x+a)(x-a) = x^2-a^2\cr
}$$
\endexample
\enddesc

%\begindesc
%\cts eqalign {}
%   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
%\cts eqalignno {}
%   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
%\cts leqalignno {}
%   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
%\explain
%^^{equation numbers}
%These commands produce a multiline math display
%in which certain corresponding parts of the lines are lined up vertically.
%The |\eqalignno| and |\leqalignno| commands also let you
%provide equation numbers for some or all of the lines.
%|\eqalignno| puts the equation numbers on the right and
%|\leqalignno| puts them on the left.
\begindesc
\cts eqalign {}
   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
\cts eqalignno {}
   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
\cts leqalignno {}
   {{\bt \rqbraces{\&lt;line&gt; \\cr $\ldots$ \&lt;line&gt; \\cr}}}
\explain
^^{å…¬å¼ç¼–å·}
è¿™äº›å‘½ä»¤æŽ’å°ä¸€ä¸ªå¤šè¡Œé™ˆåˆ—å…¬å¼ï¼Œå…¶ä¸­æŸäº›è¡Œçš„å¯¹åº”éƒ¨åˆ†ç«–ç›´å¯¹é½ã€‚
|\eqalignno| å’Œ |\leqalignno| å‘½ä»¤è¿˜å…è®¸ä½&nbsp;ç»™æŸä¸ªæˆ–æŸäº›è¡Œæ·»åŠ&nbsp;æ–¹ç¨‹ç¼–å·ã€‚
|\eqalignno| å°†æ–¹ç¨‹ç¼–å·æ”¾åœ¨å³ä¾§ï¼Œ
è€Œ |\leqalignno| å°†ç¼–å·æ”¾åœ¨å·¦ä¾§ã€‚

%Each line in the display is ended by |\cr|.  Each of the parts to be aligned
%(most often an equals sign) is preceded by
%`|&amp;|'.  An `|&amp;|' also precedes each equation number, which comes at the
%end of a line.
%You can put more than one of these commands in a single display in order
%to produce several groups of equations.  In this case, only the rightmost
%or leftmost group can be produced by |\eqalignno| or |\leqalignno|.
é™ˆåˆ—å…¬å¼çš„æ¯è¡Œç”¨ |\cr| ç»“å°¾ã€‚
å„è¡Œéœ€è¦å¯¹é½çš„å„éƒ¨åˆ†ï¼ˆå¤šåŠæ˜¯ç­‰å·ï¼‰å‰é¢åŠ&nbsp;ä¸Š `|&amp;|'ã€‚
æ–¹ç¨‹ç¼–å·æ”¾åœ¨å…¬å¼æœ«å°¾ï¼Œå®ƒçš„å‰é¢ä¹Ÿè¦åŠ&nbsp;ä¸Š `|&amp;|'ã€‚
ä½&nbsp;å¯ä»¥åœ¨å•ä¸ªé™ˆåˆ—å…¬å¼ä¸­å¤šæ¬¡ä½¿ç”¨è¿™äº›å‘½ä»¤ä»¥æŽ’å°å¤šç»„æ–¹ç¨‹ã€‚
åœ¨è¿™ç§æƒ…å½¢ä¸­ï¼Œ
åªæœ‰æœ€å³è¾¹æˆ–æœ€å·¦è¾¹çš„é‚£ç»„æ–¹ç¨‹å¯ä»¥ç”¨ |\eqalignno| æˆ– |\leqalignno| ç¼–å·ã€‚

%You can use the |\noalign| command (\xref \noalign) to change the amount
%of space between two lines of a multiline display.
%\example
%$$\left\{\eqalign{f_1(t) &amp;= 2t\cr f_2(t) &amp;= t^3\cr
%         f_3(t) &amp;= t^2-1\cr}\right\}
%  \left\{\eqalign{g_1(t) &amp;= t\cr g_2(t) &amp;= 1}\right\}$$
%|
%\dproduces
%$$\left\{\eqalign{f_1(t) &amp;= 2t\cr f_2(t) &amp;= t^3\cr
%   f_3(t) &amp;= t^2-1\cr}\right\}
%\left\{\eqalign{g_1(t) &amp;= t\cr g_2(t) &amp;= 1}\right\}$$
%\nextexample
%$$\eqalignno{
%\sigma^2&amp;=E(x-\mu)^2&amp;(12)\cr
%   &amp;={1 \over n}\sum_{i=0}^n (x_i - \mu)^2&amp;\cr
%   &amp;=E(x^2)-\mu^2\cr}$$
%|
%\produces
%\abovedisplayskip = -\baselineskip
%$$\eqalignno{
%\sigma^2&amp;=E(x-\mu)^2&amp;(12)\cr
%   &amp;={1 \over n}\sum_{i=0}^n (x_i - \mu)^2&amp;\cr
%   &amp;=E(x^2)-\mu^2\cr}$$
%\nextexample
%$$\leqalignno{
%\sigma^2&amp;=E(x-\mu)^2&amp;(6)\cr
%   &amp;=E(x^2)-\mu^2&amp;(7)\cr}$$
%|
%\produces
%\abovedisplayskip = -\baselineskip
%$$\leqalignno{
%\sigma^2&amp;=E(x-\mu)^2&amp;(6)\cr
%   &amp;=E(x^2)-\mu^2&amp;(7)\cr}$$
%\nextexample
%$$\eqalignno{
%  &amp;(x+a)^2 = x^2+2ax+a^2&amp;(19)\cr
%  &amp;(x+a)(x-a) = x^2-a^2\cr}$$
%% same effect as \displaylines but with an equation number
%|
%\dproduces
%$$\eqalignno{
%&amp;(x+a)^2 = x^2+2ax+a^2&amp;(19)\cr
%&amp;(x+a)(x-a) = x^2-a^2\cr
%}$$
%% same effect as \displaylines but with an equation number
ä½&nbsp;å¯ä»¥ä½¿ç”¨ |\noalign| å‘½ä»¤ï¼ˆ\xref\noalign ï¼‰æ”¹å˜å¤šè¡Œé™ˆåˆ—å…¬å¼ä¸­ä¸¤è¡Œçš„é—´éš”ã€‚
\example
$$\left\{\eqalign{f_1(t) &amp;= 2t\cr f_2(t) &amp;= t^3\cr
         f_3(t) &amp;= t^2-1\cr}\right\}
  \left\{\eqalign{g_1(t) &amp;= t\cr g_2(t) &amp;= 1}\right\}$$
|
\dproduces
$$\left\{\eqalign{f_1(t) &amp;= 2t\cr f_2(t) &amp;= t^3\cr
   f_3(t) &amp;= t^2-1\cr}\right\}
\left\{\eqalign{g_1(t) &amp;= t\cr g_2(t) &amp;= 1}\right\}$$
\nextexample
$$\eqalignno{
\sigma^2&amp;=E(x-\mu)^2&amp;(12)\cr
   &amp;={1 \over n}\sum_{i=0}^n (x_i - \mu)^2&amp;\cr
   &amp;=E(x^2)-\mu^2\cr}$$
|
\produces
\abovedisplayskip = -\baselineskip
$$\eqalignno{
\sigma^2&amp;=E(x-\mu)^2&amp;(12)\cr
   &amp;={1 \over n}\sum_{i=0}^n (x_i - \mu)^2&amp;\cr
   &amp;=E(x^2)-\mu^2\cr}$$
\nextexample
$$\leqalignno{
\sigma^2&amp;=E(x-\mu)^2&amp;(6)\cr
   &amp;=E(x^2)-\mu^2&amp;(7)\cr}$$
|
\produces
\abovedisplayskip = -\baselineskip
$$\leqalignno{
\sigma^2&amp;=E(x-\mu)^2&amp;(6)\cr
   &amp;=E(x^2)-\mu^2&amp;(7)\cr}$$
\nextexample
$$\eqalignno{
  &amp;(x+a)^2 = x^2+2ax+a^2&amp;(19)\cr
  &amp;(x+a)(x-a) = x^2-a^2\cr}$$
% same effect as \displaylines but with an equation number
|
\dproduces
$$\eqalignno{
&amp;(x+a)^2 = x^2+2ax+a^2&amp;(19)\cr
&amp;(x+a)(x-a) = x^2-a^2\cr
}$$
% same effect as \displaylines but with an equation number

%\eix^^{displays//multiline}
%\endexample
%\enddesc
\eix^^{é™ˆåˆ—å…¬å¼//å¤šè¡Œé™ˆåˆ—å…¬å¼}
\endexample
\enddesc


%==========================================================================
%\section {Fonts in math formulas}
\section {æ•°å­¦å…¬å¼å­—ä½“}

%\begindesc
%^^{fonts}
%\xrdef{mathfonts}
%%
%\easy\ctsx cal {use calligraphic uppercase font}
%\ctsx mit {use math italic font}
%\ctsx oldstyle {use old style digit font}
%\explain
%These commands cause \TeX\ to typeset the following text in the
%specified font.  You can only use them in \minref{math mode}.
%The |\mit| command is useful for producing slanted capital ^{Greek letters}.
%You can also use the commands given in
%\headcit{Selecting fonts}{selfont} to change fonts in math mode.
%\example
%${\cal XYZ} \quad
%{\mit AaBb\Gamma \Delta \Sigma} \quad
%{\oldstyle 0123456789}$
%|
%\produces
%${\cal XYZ} \quad
%{\mit AaBb\Gamma \Delta \Sigma} \quad
%{\oldstyle 0123456789}$
%\endexample
%\enddesc
\begindesc
^^{å­—ä½“}
\xrdef{mathfonts}
%
\easy\ctsx cal {use calligraphic uppercase font}
\ctsx mit {use math italic font}
\ctsx oldstyle {use old style digit font}
\explain
è¿™äº›å‘½ä»¤è®© \TeX\ ç”¨æŒ‡å®šçš„å­—ä½“æŽ’ç‰ˆä¹‹åŽçš„æ–‡æœ¬ã€‚
ä½&nbsp;åªèƒ½åœ¨\minref{æ•°å­¦æ¨¡å¼}ä¸­ä½¿ç”¨å®ƒä»¬ã€‚
|\mit| å‘½ä»¤å¯ç”¨äºŽæŽ’å°æ–œä½“å¤§å†™^{å¸Œè…Šå­—æ¯}ã€‚
ä½&nbsp;è¿˜å¯ä»¥ç”¨\headcit{é€‰æ‹©å­—ä½“}{selfont}ä¸­çš„é‚£äº›å‘½ä»¤æ”¹å˜æ•°å­¦æ¨¡å¼ä¸­çš„å­—ä½“ã€‚
\example
${\cal XYZ} \quad
{\mit AaBb\Gamma \Delta \Sigma} \quad
{\oldstyle 0123456789}$
|
\produces
${\cal XYZ} \quad
{\mit AaBb\Gamma \Delta \Sigma} \quad
{\oldstyle 0123456789}$
\endexample
\enddesc

%^^{type styles}
%\begindesc
%\ctsx itfam {family for italic type}
%\ctsx bffam {family for boldface type}
%\ctsx slfam {family for slanted type}
%\ctsx ttfam {family for typewriter type}
%\explain
%These commands define type families \minrefs{family} for use in
%\minref{math mode}.  Their principal use is in defining the
%|\it|, |\bf|, |\sl|, and |\tt| commands so that they work in math mode.
%\enddesc
^^{å­—ä½“é£Žæ&nbsp;¼}
\begindesc
\ctsx itfam {family for italic type}
\ctsx bffam {family for boldface type}
\ctsx slfam {family for slanted type}
\ctsx ttfam {family for typewriter type}
\explain
è¿™äº›å‘½ä»¤å®šä¹‰å‡&nbsp;ç§ç”¨äºŽ\minref{æ•°å­¦æ¨¡å¼}çš„å­—ä½“æ—\minrefs{æ—}ã€‚
å®ƒä»¬ä¸»è¦ç”¨åœ¨ |\it|ã€|\bf|ã€|\sl| å’Œ |\tt| å‘½ä»¤çš„å®šä¹‰ä¸­ï¼Œä½¿è¿™äº›å‘½ä»¤èƒ½åœ¨æ•°å­¦æ¨¡å¼ä¸­ä½¿ç”¨ã€‚
\enddesc

%\begindesc
%\cts fam {\param{number}}
%\explain
%When \TeX\ is in \minref{math mode}, it ordinarily typesets a character
%using the font family ^^{class} given in its \minref{mathcode}.
%^^{family//given by \b\tt\\fam\e}
%However, when \TeX\ is in math mode and encounters a character whose
%\minref{class} is $7$ (Variable), it typesets that character using
%the font \minref{family} given by the value of |\fam|, provided that the
%value of |\fam| is between $0$ and $15$.
%If the value of |\fam| isn't in that range, \TeX\ uses the family in
%the character's mathcode as in the ordinary case.
%\TeX\ sets |\fam| to $-1$ whenever it enters math mode.
%Outside of math mode, |\fam| has no effect.
\begindesc
\cts fam {\param{number}}
\explain
åœ¨\minref{æ•°å­¦æ¨¡å¼}æ—¶ï¼Œ\TeX\ é€šå¸¸ç”¨å­—ç¬¦çš„\minref{æ•°å­¦ç&nbsp;}æŒ‡å®šçš„å­—ä½“æ—æŽ’ç‰ˆè¯¥å­—ç¬¦ã€‚
^^{ç±»}^^{æ—//ç”¨ \b\tt\\fam\e ç»™å‡º}
ä½†æ˜¯ï¼Œå¦‚æžœ \TeX\ åœ¨æ•°å­¦æ¨¡å¼ä¸­é‡åˆ°ç¬¬ $7$ \minref{ç±»}ï¼ˆå˜é‡ï¼‰å­—ç¬¦ï¼Œ
å®ƒå°†ç”¨ç”± |\fam| çš„å€¼ç»™å‡ºçš„å­—ä½“\minref{æ—}æŽ’ç‰ˆè¯¥å­—ç¬¦ï¼Œ
åªè¦ |\fam| çš„å€¼åœ¨ $0$ å’Œ $15$ ä¹‹é—´ã€‚
å¦‚æžœ |\fam| çš„å€¼ä¸åœ¨è¯¥èŒƒå›´å†…ï¼Œ
\TeX\ å°±åƒé€šå¸¸æƒ…å½¢é‚£æ&nbsp;·ä½¿ç”¨å­—ç¬¦çš„æ•°å­¦ç&nbsp;æŒ‡å®šçš„å­—ä½“æ—ã€‚
\TeX\ åœ¨è¿›å…¥æ•°å­¦æ¨¡å¼æ—¶è®¾å®š |\fam| ä¸º $-1$ã€‚
åœ¨æ•°å­¦æ¨¡å¼ä¹‹å¤–ï¼Œ|\fam| æ—&nbsp;ä»»ä½•æ•ˆæžœã€‚

%By assigning a value to
%|\fam| you can change the way that \TeX\ typesets ordinary
%characters such as variables.
%For instance, by setting |\fam| to |\ttfam|, you cause \TeX\ to typeset
%variables using a typewriter font.
%\PlainTeX\ defines |\tt| as a \minref{macro} that, among other things,
%sets |\fam| to |\ttfam|.
%\example
%\def\bf{\fam\bffam\tenbf} % As in plain TeX.
%|
%\endexample
%\enddesc
é€šè¿‡èµ‹äºˆ |\fam| ä¸åŒçš„å€¼ï¼Œä½&nbsp;èƒ½è®© \TeX\ ç”¨ä¸åŒæ–¹å¼æŽ’ç‰ˆæ™®é€šå­—ç¬¦ï¼Œæ¯”å¦‚å˜é‡ã€‚
ä¸¾ä¸ªä¾‹å­ï¼Œè®¾å®šäº† |\fam| ä¸º |\ttfam| ï¼Œä½&nbsp;å¯ä»¥è®© \TeX\ ç”¨æ‰“å­—æœºå­—ä½“æŽ’ç‰ˆå˜é‡ã€‚
\PlainTeX\ åœ¨å®šä¹‰ |\tt| \minref{å®}æ—¶ï¼Œé™¤äº†å…¶ä»–è®¾å®šä¹‹å¤–ï¼Œ
è¿˜è®¾å®š |\fam| ç­‰äºŽ |\ttfam|ã€‚
\example
\def\bf{\fam\bffam\tenbf} % As in plain TeX.
|
\endexample
\enddesc

%\begindesc
%\cts textfont {\&lt;family&gt;\param{fontname}}
%\cts scriptfont {\&lt;family&gt;\param{fontname}}
%\cts scriptscriptfont {\&lt;family&gt;\param{fontname}}
%\explain
%^^{text style}
%^^{script style}
%^^{scriptscript style}
%Each of these parameters specifies the font that \TeX\ is to use for
%typesetting the indicated \minref{style} in the indicated \minref{family}.
%These choices have no effect outside of \minref{math mode}.
%\example
%\scriptfont2 = \sevensy % As in plain TeX.
%|
%\endexample
%\enddesc
\begindesc
\cts textfont {\&lt;family&gt;\param{fontname}}
\cts scriptfont {\&lt;family&gt;\param{fontname}}
\cts scriptscriptfont {\&lt;family&gt;\param{fontname}}
\explain
^^{æ–‡æœ¬æ&nbsp;·å¼}
^^{æ&nbsp;‡å·æ&nbsp;·å¼}
^^{å°æ&nbsp;‡å·æ&nbsp;·å¼}
è¿™ä¸‰ä¸ªå‚æ•°åˆ†åˆ«é€‰æ‹© \TeX\ æŽ’ç‰ˆæŒ‡å®š\minref{æ—}çš„æŒ‡å®š\minref{æ&nbsp;·å¼}æ—¶æ‰€ç”¨çš„å­—ä½“ã€‚
è¿™äº›é€‰æ‹©åœ¨\minref{æ•°å­¦æ¨¡å¼}ä¹‹å¤–æ—&nbsp;ä»»ä½•æ•ˆæžœã€‚
\example
\scriptfont2 = \sevensy % As in plain TeX.
|
\endexample
\enddesc

%\see ``Type styles'' (\xref{seltype}).
\see ``å­—ä½“é£Žæ&nbsp;¼''ï¼ˆ\xref{seltype}ï¼‰ã€‚


%==========================================================================
%\section {Constructing math symbols}
\section {æž„é€&nbsp;æ•°å­¦ç¬¦å·}

%==========================================================================
%\subsection {Making delimiters bigger}
\subsection {å¢žå¤§å®šç•Œç¬¦}

%\begindesc
%\makecolumns 16/4:
%\easy\cts big {}
%\cts bigl {}
%\cts bigm {}
%\cts bigr {}
%\cts Big {}
%\cts Bigl {}
%\cts Bigm {}
%\cts Bigr {}
%\cts bigg {}
%\cts biggl {}
%\cts biggm {}
%\cts biggr {}
%\cts Bigg {}
%\cts Biggl {}
%\cts Biggm {}
%\cts Biggr {}
%\explain
%^^{delimiters//enlarging}
%These commands make \minref{delimiter}s bigger than their normal size.
%The commands in the four columns
%produce successively larger sizes.  The difference between |\big|,
%|\bigl|, |\bigr|, and |bigm| has to do with the \minref{class} of the
%enlarged delimiter:
%\ulist\compact
%\li |\big| produces an ordinary symbol.
%\li |\bigl| produces an opening symbol.
%\li |\bigr| produces a closing symbol.
%\li |\bigm| produces a relation symbol.
%\endulist
%\noindent
%\TeX\ uses the class of a symbol in order to decide how much space to put
%around that symbol.
\begindesc
\makecolumns 16/4:
\easy\cts big {}
\cts bigl {}
\cts bigm {}
\cts bigr {}
\cts Big {}
\cts Bigl {}
\cts Bigm {}
\cts Bigr {}
\cts bigg {}
\cts biggl {}
\cts biggm {}
\cts biggr {}
\cts Bigg {}
\cts Biggl {}
\cts Biggm {}
\cts Biggr {}
\explain
^^{å®šç•Œç¬¦//å¢žå¤§å®šç•Œç¬¦}
è¿™äº›å‘½ä»¤è®©\minref{å®šç•Œç¬¦}æ¯”å®ƒä»¬çš„æ­£å¸¸å°ºå¯¸è¿˜å¤§ã€‚
è¿™å››æ&nbsp;ä¸­çš„å‘½ä»¤ç”Ÿæˆä¾æ¬¡å¢žå¤§çš„å°ºå¯¸ã€‚|\big|ã€|\bigl|ã€|\bigr|
å’Œ |\bigm| çš„åŒºåˆ«åœ¨äºŽå¢žå¤§çš„å®šç•Œç¬¦æ‰€å±žçš„\minref{ç±»}ï¼š
\ulist\compact
\li |\big| ç”Ÿæˆä¸€ä¸ªæ™®é€šç¬¦å·ã€‚
\li |\bigl| ç”Ÿæˆä¸€ä¸ªå¼€ç¬¦å·ã€‚
\li |\bigr| ç”Ÿæˆä¸€ä¸ªé—­ç¬¦å·ã€‚
\li |\bigm| ç”Ÿæˆä¸€ä¸ªå…³ç³»ç¬¦å·ã€‚
\endulist
\noindent
\TeX\ ä»Žå­—ç¬¦æ‰€å±žçš„ç±»ç¡®å®šè¦åœ¨è¯¥å­—ç¬¦ä¸¤è¾¹ç•™ä¸‹å¤šå¤§çš„ç©ºæ&nbsp;¼ã€‚

%These commands, unlike |\left| and |\right|,
%do \emph{not} define a group.

%\example
%$$(x) \quad \bigl(x\bigr) \quad \Bigl(x\Bigr) \quad
%   \biggl(x\biggr) \quad \Biggl(x\Biggr)\qquad
%[x] \quad \bigl[x\bigr] \quad \Bigl[x\Bigr] \quad
%   \biggl[x\biggr] \quad \Biggl[x\Biggr]$$
%|
%\dproduces
%$$(x) \quad \bigl(x\bigr) \quad \Bigl(x\Bigr) \quad
%\biggl(x\biggr) \quad \Biggl(x\Biggr)\qquad
%[x] \quad \bigl[x\bigr] \quad \Bigl[x\Bigr] \quad
%\biggl[x\biggr] \quad \Biggl[x\Biggr]$$
%\endexample
%\enddesc
\example
$$(x) \quad \bigl(x\bigr) \quad \Bigl(x\Bigr) \quad
   \biggl(x\biggr) \quad \Biggl(x\Biggr)\qquad
[x] \quad \bigl[x\bigr] \quad \Bigl[x\Bigr] \quad
   \biggl[x\biggr] \quad \Biggl[x\Biggr]$$
|
\dproduces
$$(x) \quad \bigl(x\bigr) \quad \Bigl(x\Bigr) \quad
\biggl(x\biggr) \quad \Biggl(x\Biggr)\qquad
[x] \quad \bigl[x\bigr] \quad \Bigl[x\Bigr] \quad
\biggl[x\biggr] \quad \Biggl[x\Biggr]$$
\endexample
\enddesc

%==========================================================================
%\subsection {Parts of large symbols}
\subsection {å¤§ç¬¦å·çš„ä¸€éƒ¨åˆ†}

%\begindesc
%\cts downbracefill {}
%\cts upbracefill {}
%\explain
%These commands respectively produce upward-pointing
%and downward-pointing extensible ^{horizontal braces}. ^^{braces}
%\TeX\ will make the braces as wide as necessary.
%These commands
%are used in the definitions of ^|\overbrace| and ^|\underbrace|
%(\xref \overbrace).
%\example
%$$\hbox to 1in{\downbracefill} \quad
%   \hbox to 1in{\upbracefill}$$
%|
%\dproduces
%$$\hbox to 1in{\downbracefill} \quad
%   \hbox to 1in{\upbracefill}$$
%\endexample
%\enddesc
\begindesc
\cts downbracefill {}
\cts upbracefill {}
\explain
è¿™ä¸¤ä¸ªå‘½ä»¤åˆ†åˆ«æŽ’å°æœä¸Šå’Œæœä¸‹çš„å¯ä¼¸å±•^{æ°´å¹³èŠ±æ‹¬å·}ã€‚^^{èŠ±æ‹¬å·}
\TeX\ å°†è®©èŠ±æ‹¬å·è¶³å¤Ÿå®½ã€‚
è¿™ä¸¤ä¸ªå‘½ä»¤ç”¨äºŽå®šä¹‰ ^|\overbrace| å’Œ ^|\underbrace|ï¼ˆ\xref\overbrace ï¼‰ã€‚
\example
$$\hbox to 1in{\downbracefill} \quad
   \hbox to 1in{\upbracefill}$$
|
\dproduces
$$\hbox to 1in{\downbracefill} \quad
   \hbox to 1in{\upbracefill}$$
\endexample
\enddesc

%\begindesc
%\cts arrowvert {}
%\cts Arrowvert {}
%\cts lmoustache {}
%\cts rmoustache {}
%\cts bracevert {}
%\explain
%These commands produce portions of certain large
%delimiters
%^^{delimiters//parts of}
%and can themselves be used as delimiters.
%They refer to characters in the ^|cmex10| math font.
%\example
%$$\cdots \Big\arrowvert \cdots \Big\Arrowvert \cdots
%  \Big\lmoustache \cdots \Big\rmoustache \cdots
%  \Big\bracevert \cdots$$
%|
%\dproduces
%$$\cdots \Big\arrowvert \cdots \Big\Arrowvert \cdots
%  \Big\lmoustache \cdots \Big\rmoustache \cdots
%  \Big\bracevert \cdots$$
%\endexample
%\enddesc
\begindesc
\cts arrowvert {}
\cts Arrowvert {}
\cts lmoustache {}
\cts rmoustache {}
\cts bracevert {}
\explain
è¿™äº›å‘½ä»¤æŽ’å°æŸäº›å¤§å®šç•Œç¬¦çš„ä¸€éƒ¨åˆ†ï¼Œ
^^{å®šç•Œç¬¦//å®šç•Œç¬¦çš„ä¸€éƒ¨åˆ†}
æŠŠå®ƒä»¬ä¹Ÿç”¨ä½œå®šç•Œç¬¦ã€‚
å®ƒä»¬å–è‡ª ^|cmex10| æ•°å­¦å­—ä½“ä¸­çš„å­—ç¬¦ã€‚
\example
$$\cdots \Big\arrowvert \cdots \Big\Arrowvert \cdots
  \Big\lmoustache \cdots \Big\rmoustache \cdots
  \Big\bracevert \cdots$$
|
\dproduces
$$\cdots \Big\arrowvert \cdots \Big\Arrowvert \cdots
  \Big\lmoustache \cdots \Big\rmoustache \cdots
  \Big\bracevert \cdots$$
\endexample
\enddesc


%==========================================================================
%\section {Aligning parts of a formula}
\section {å¯¹é½éƒ¨åˆ†å…¬å¼}

%==========================================================================
%\subsection {Aligning accents}
\subsection {å¯¹é½æ•°å­¦é‡éŸ³}

%\begindesc
%\bix^^{accents//aligning}
%\cts skew {\&lt;number&gt; \&lt;argument$_1$&gt; \&lt;argument$_2$&gt;}
%\explain
%This command shifts the accent \&lt;argument$_1$&gt; by
%\&lt;number&gt; \minref{mathematical unit}s to the right of its normal position
%with respect to \&lt;argu\-ment$_2$&gt;.
%The most common use of this command is for
%modifying the position of an accent that's over
%another accent.
%\example
%$$\skew 2\bar{\bar z}\quad\skew 3\tilde{\tilde y}\quad
%  \skew 4\tilde{\hat x}$$
%|
%\dproduces
%$$\skew 2\bar{\bar z}\quad\skew 3\tilde{\tilde y}\quad
%  \skew 4\tilde{\hat x}$$
%\endexample
%\enddesc
\begindesc
\bix^^{é‡éŸ³//å¯¹é½é‡éŸ³}
\cts skew {\&lt;number&gt; \&lt;argument$_1$&gt; \&lt;argument$_2$&gt;}
\explain
æ­¤å‘½ä»¤å°†é‡éŸ³ \&lt;argument$_1$&gt; ç›¸å¯¹ \&lt;argu\-ment$_2$&gt;
ä»Žå®ƒçš„æ­£å¸¸ä½ç½®å¾€å³ç§»åŠ¨ \&lt;number&gt; ä¸ª\minref{æ•°å­¦å•ä½}ã€‚
æ­¤å‘½ä»¤å¸¸ç”¨äºŽè°ƒæ•´åœ¨å…¶ä»–é‡éŸ³ä¹‹ä¸Šçš„é‡éŸ³çš„ä½ç½®ã€‚
\example
$$\skew 2\bar{\bar z}\quad\skew 3\tilde{\tilde y}\quad
  \skew 4\tilde{\hat x}$$
|
\dproduces
$$\skew 2\bar{\bar z}\quad\skew 3\tilde{\tilde y}\quad
  \skew 4\tilde{\hat x}$$
\endexample
\enddesc

%\begindesc
%\cts skewchar {\&lt;font&gt;\param{number}}
%\explain
%The |\skewchar| of a font
%is the character in the font whose kerns,
%as defined in the font's metrics file, determine the positions
%of math accents. That is, suppose that \TeX\ is applying a math accent
%to the character `|x|'.  \TeX\ checks if the character pair
%`|x\skewchar|' has a kern; if so, it moves the accent by the amount of
%that kern. The complete algorithm that \TeX\ uses to position math
%accents (which involves many more things) is in \knuth{Appendix~G}.
\begindesc
\cts skewchar {\&lt;font&gt;\param{number}}
\explain
å­—ä½“çš„ |\skewchar| æ˜¯å­—ä½“ä¸­çš„æŸä¸ªå­—ç¬¦ï¼Œ
å®ƒåœ¨å­—ä½“åº¦é‡æ–‡ä»¶ä¸­å®šä¹‰çš„ç´§æŽ’ç¡®å®šäº†æ•°å­¦é‡éŸ³çš„ä½ç½®ã€‚
ä¹Ÿå°±æ˜¯è¯´ï¼Œå‡è®¾ \TeX\ è¦ç»™å­—ç¬¦ `|x|' åŠ&nbsp;ä¸Šæ•°å­¦é‡éŸ³ï¼Œ
åˆ™ \TeX\ æ£€æŸ¥å­—ç¬¦å¯¹ `|x\skewchar|' æ˜¯å¦æœ‰ä¸ªç´§æŽ’ï¼›
å¦‚æžœæœ‰ï¼Œå®ƒå°±ä»¥è¯¥ç´§æŽ’çš„å€¼ç§»åŠ¨è¯¥é‡éŸ³ã€‚
\TeX\ æ”¾ç½®æ•°å­¦é‡éŸ³çš„å®Œæ•´ç®—æ³•ï¼ˆè¿™æ¶‰åŠåˆ°å¾ˆå¤šäº‹æƒ…ï¼‰åœ¨\knuth{é™„å½•~G}ä¸­æè¿°ã€‚

%If the value of |\skewchar| is not in the range $0$--$255$,
%\TeX\ takes the kern value to be zero.
å¦‚æžœ |\skewchar| çš„å€¼ä¸åœ¨ $0$--$255$ çš„èŒƒå›´å†…ï¼Œ\TeX\ å°†ç´§æŽ’çš„å€¼å½“ä½œé›¶ã€‚

%Note that \&lt;font&gt; is a control sequence
%that names a font, not a \&lt;font\-name&gt; that names font files.
%Beware:
%an assignment to |\skewchar| is \emph{not} undone at the end
%of a group.
%If you want to change |\skewchar| locally, you'll need to
%save and restore its original value explicitly.
%\enddesc
æ³¨æ„ \&lt;font&gt; æ˜¯ä¸€ä¸ªæŽ§åˆ¶åºåˆ—ï¼Œå®ƒæ˜¯å­—ä½“çš„åç§°ï¼Œè€Œä¸æ˜¯å­—ä½“æ–‡ä»¶çš„åç§° \&lt;font\-name&gt;ã€‚
å°å¿ƒï¼šå¯¹ |\skewchar| çš„èµ‹å€¼åœ¨ç¼–ç»„ç»“æŸæ—¶\emph{å¹¶ä¸ä¼š}è¿˜åŽŸã€‚
å¦‚æžœä½&nbsp;æƒ³å±€éƒ¨æ”¹å˜|\skewchar|ï¼Œä½&nbsp;éœ€è¦æ˜¾å¼åœ°ä¿å­˜å’Œè¿˜åŽŸå®ƒçš„åŽŸå§‹å€¼ã€‚
\enddesc

%\begindesc
%\cts defaultskewchar {\param{number}}
%\explain
%When \TeX\ reads the metrics file
%^^{metrics file//default skew character in}
%for a font in response to a
%^|\font| command, it sets the font's ^|\skewchar| to
%|\default!-skewchar|.
%If the value of |\default!-skewchar| is
%not in the range $0$--$255$, \TeX\ does not assign any
%skew characters by default.
%\PlainTeX\ sets |\defaultskewchar| to $-1$, and it's usually best
%to leave it there.
%\margin{Misleading example deleted.}
%\eix^^{accents//aligning}
%\enddesc
\begindesc
\cts defaultskewchar {\param{number}}
\explain
åœ¨æ‰§è¡Œ ^|\font| å‘½ä»¤è¯»å–å­—ä½“çš„åº¦é‡æ–‡ä»¶æ—¶ï¼Œ
^^{åº¦é‡æ–‡ä»¶//å…¶ä¸­çš„é»˜è®¤æ–œå­—ç¬¦}
\TeX\ è®¾å®šè¯¥å­—ä½“çš„ ^|\skewchar| ç­‰äºŽ |\default!-skewchar|ã€‚
å¦‚æžœ |\default!-skewchar| çš„å€¼ä¸åœ¨ $0$--$255$ çš„èŒƒå›´å†…ï¼Œ
\TeX\ é»˜è®¤å°±ä¸è®¾å®š |\skewchar| çš„å€¼ã€‚
\PlainTeX\ è®¾å®š |\defaultskewchar| ç­‰äºŽ $-1$ï¼Œä¸€èˆ¬ä¸éœ€è¦æ”¹åŠ¨å®ƒã€‚
\margin{Misleading example deleted.}
\eix^^{é‡éŸ³//å¯¹é½é‡éŸ³}
\enddesc

%==========================================================================
%\subsection {Aligning material vertically}
\subsection {ç«–ç›´å¯¹é½ç´&nbsp;æ}

%\begindesc
%\cts vcenter {\rqbraces{\&lt;vertical mode material&gt;}}
%\ctsbasic {\\vcenter to \&lt;dimen&gt; \rqbraces{\&lt;vertical mode material&gt;}}{}
%\ctsbasic {\\vcenter spread \&lt;dimen&gt; \rqbraces{\&lt;vertical mode material&gt;}}{}
%\explain
%Every math formula has an invisible
%``^{axis}'' that \TeX\ treats as a kind of
%horizontal centering line for that formula.
%For instance, the axis of a formula consisting of a
%fraction is at the center of the fraction bar.
%The |\vcenter| command tells \TeX\ to place the \&lt;vertical mode material&gt;
%in a \minref{vbox} and to center the vbox
%with respect to the axis of the formula it is currently constructing.
\begindesc
\cts vcenter {\rqbraces{\&lt;vertical mode material&gt;}}
\ctsbasic {\\vcenter to \&lt;dimen&gt; \rqbraces{\&lt;vertical mode material&gt;}}{}
\ctsbasic {\\vcenter spread \&lt;dimen&gt; \rqbraces{\&lt;vertical mode material&gt;}}{}
\explain
æ¯ä¸ªæ•°å­¦å…¬å¼éƒ½æœ‰ä¸€ä¸ªä¸å¯è§çš„``^{è½´çº¿}''ï¼Œ\TeX\ å°†å®ƒä½œä¸ºè¯¥å…¬å¼çš„æ°´å¹³ä¸­å¿ƒçº¿ã€‚
ä¸¾ä¸ªä¾‹å­ï¼Œç”±åˆ†å¼ç»„æˆçš„å…¬å¼çš„è½´çº¿å°±åœ¨åˆ†æ•°çº¿çš„ä¸­å¿ƒã€‚
|\vcenter| å‘½ä»¤è®© \TeX\ å°† \&lt;vertical mode material&gt; æ”¾å…¥\minref{ç«–ç›´ç›’å­}ä¸­ï¼Œ
å¹¶å°†è¯¥ç«–ç›´ç›’å­ä¸Žå½“å‰å…¬å¼çš„è½´çº¿å±…ä¸­å¯¹é½ã€‚

%The first form of the command
%centers the material as given.  The second and third
%forms expand or shrink the material vertically as in the |\vbox| command
%(\xref \vbox).
æ­¤å‘½ä»¤çš„ç¬¬ä¸€ç§å½¢å¼å¦‚ä¸Šæ‰€è¿°å±…ä¸­æ”¾ç½®ç´&nbsp;æã€‚
åŽä¸¤ç§å½¢å¼ç«–ç›´æ‰©å±•æˆ–æ”¶ç¼©ç´&nbsp;æï¼Œå¦‚åŒ |\vbox| å‘½ä»¤ï¼ˆ\xref\vbox ï¼‰ã€‚

%\example
%$${n \choose k} \buildrel \rm def \over \equiv \&gt;
%\vcenter{\hsize 1.5 in \noindent the number of
%combinations of $n$ things taken $k$ at a time}$$
%|
%\dproduces
%$${n \choose k} \buildrel \rm def \over \equiv \&gt;
%\vcenter{\hsize 1.5 in \noindent the number of
%combinations of $n$ things taken $k$ at a time}$$
%\endexample
%\enddesc
\example
$${n \choose k} \buildrel \rm def \over \equiv \&gt;
\vcenter{\hsize 1.5 in \noindent the number of
combinations of $n$ things taken $k$ at a time}$$
|
\dproduces
$${n \choose k} \buildrel \rm def \over \equiv \&gt;
\vcenter{\hsize 1.5 in \noindent the number of
combinations of $n$ things taken $k$ at a time}$$
\endexample
\enddesc


%==========================================================================
%\section {Producing spaces}
\section {ç”Ÿæˆé—´éš”}

%==========================================================================
%\subsection {Fixed-width math spaces}
\subsection {å›ºå®šå®½åº¦æ•°å­¦é—´éš”}

%\begindesc
%\bix^^{space//in math formulas}
%\ctspecial ! \ctsxrdef{@shriek}
%\ctspecial , \ctsxrdef{@comma}
%\ctspecial &gt; \ctsxrdef{@greater}
%\ctspecial ; \ctsxrdef{@semi}
%\explain
%These commands produce various amounts of ^{extra space} in formulas.  They
%are defined in terms of \minref{mathematical unit}s, so \TeX\ adjusts
%the amount of space according to the current \minref{style}.
%\ulist
%\li |\!!| produces a negative thin space, i.e., it reduces the space
%between its neighboring subformulas by the amount of a thin space.
%\li |\,| produces a thin space.
%\li |\&gt;| produces a medium space.
%\li |\;| produces a thick space.
%\endulist
%\example
%$$00\quad0\!!0\quad0\,0\quad0\&gt;0\quad0\;0\quad
%{\scriptstyle 00\quad0\!!0\quad0\,0\quad0\&gt;0\quad0\;0}$$
%|
%\dproduces
%$$00\quad0\!0\quad0\,0\quad0\&gt;0\quad0\;0\quad
%{\scriptstyle 00\quad0\!0\quad0\,0\quad0\&gt;0\quad0\;0}$$
%\endexample
%\enddesc
\begindesc
\bix^^{é—´éš”//æ•°å­¦å…¬å¼ä¸­çš„é—´éš”}
\ctspecial ! \ctsxrdef{@shriek}
\ctspecial , \ctsxrdef{@comma}
\ctspecial &gt; \ctsxrdef{@greater}
\ctspecial ; \ctsxrdef{@semi}
\explain
è¿™äº›å‘½ä»¤åœ¨å…¬å¼ä¸­ç”Ÿæˆå„ç§å¤§å°çš„^{é¢å¤–é—´éš”}ã€‚
å®ƒä»¬ä½¿ç”¨\minref{æ•°å­¦å•ä½}æ¥å®šä¹‰ï¼Œ
å›&nbsp;æ­¤ \TeX\ ä¼šæ&nbsp;¹æ®å½“å‰\minref{æ&nbsp;·å¼}è°ƒæ•´é—´éš”çš„å¤§å°ã€‚
\ulist
\li |\!!| ç”Ÿæˆè´Ÿçš„ç»†å°é—´éš”ï¼Œå³å®ƒè®©ç›¸é‚»å­å…¬å¼çš„é—´éš”å‡åŽ»è¯¥ç»†å°é—´éš”çš„å¤§å°ã€‚
\li |\,| ç”Ÿæˆç»†å°é—´éš”ã€‚
\li |\&gt;| ç”Ÿæˆä¸­ç­‰é—´éš”ã€‚
\li |\;| ç”Ÿæˆè¾ƒå¤§é—´éš”ã€‚
\endulist
\example
$$00\quad0\!!0\quad0\,0\quad0\&gt;0\quad0\;0\quad
{\scriptstyle 00\quad0\!!0\quad0\,0\quad0\&gt;0\quad0\;0}$$
|
\dproduces
$$00\quad0\!0\quad0\,0\quad0\&gt;0\quad0\;0\quad
{\scriptstyle 00\quad0\!0\quad0\,0\quad0\&gt;0\quad0\;0}$$
\endexample
\enddesc

%\begindesc
%\cts thinmuskip {\param{muglue}}
%\cts medmuskip {\param{muglue}}
%\cts thickmuskip {\param{muglue}}
%\explain
%These parameters define thin, medium, and thick spaces in
%math mode.
%\example
%$00\quad0\mskip\thinmuskip0\quad0\mskip\medmuskip0
%   \quad0\mskip\thickmuskip0$
%|
%\produces
%$00\quad0\mskip\thinmuskip0\quad0\mskip\medmuskip0
%   \quad0\mskip\thickmuskip0$
%\endexample
%\enddesc
\begindesc
\cts thinmuskip {\param{muglue}}
\cts medmuskip {\param{muglue}}
\cts thickmuskip {\param{muglue}}
\explain
è¿™äº›å‚æ•°å®šä¹‰äº†æ•°å­¦æ¨¡å¼ä¸­ç»†å°ã€ä¸­ç­‰å’Œè¾ƒå¤§é—´éš”çš„å¤§å°ã€‚
\example
$00\quad0\mskip\thinmuskip0\quad0\mskip\medmuskip0
   \quad0\mskip\thickmuskip0$
|
\produces
$00\quad0\mskip\thinmuskip0\quad0\mskip\medmuskip0
   \quad0\mskip\thickmuskip0$
\endexample
\enddesc

%\begindesc
%\cts jot {\param{dimen}}
%\explain
%This parameter defines a distance that is equal to three points (unless
%you change it).
%The |\jot| is a convenient unit of measure for opening up \hbox{math displays}.
%\enddesc
\begindesc
\cts jot {\param{dimen}}
\explain
æ­¤å‚æ•°å®šä¹‰ä¸ºä¸‰ä¸ªç‚¹çš„è·ç¦»ï¼ˆé™¤éžä½&nbsp;æ”¹å˜äº†å®ƒï¼‰ã€‚
åœ¨ç”¨ |\openup| å‘½ä»¤åˆ†å¼€é™ˆåˆ—å…¬å¼å„è¡Œæ—¶ï¼Œ|\jot| æ˜¯ä¸€ä¸ªå®žç”¨çš„åº¦é‡å•ä½ã€‚
\footnote{è¯‘æ³¨ï¼šä¸‹é¢çš„ä¾‹å­ä¸ºè¯‘è€…æ‰€åŠ&nbsp;ã€‚è¯·å‚é˜… |\openup| å‘½ä»¤ï¼ˆ\xref\openup ï¼‰ã€‚}
\example
$$\vbox{\halign{$\hfil#\hfil$\cr x\cr y\cr}}$$
$$\openup2\jot\vbox{\halign{$\hfil#\hfil$\cr x\cr y\cr}}$$
|
\produces
$$\vbox{\halign{$\hfil#\hfil$\cr x\cr y\cr}}$$
$$\openup2\jot\vbox{\halign{$\hfil#\hfil$\cr x\cr y\cr}}$$
\endexample
\enddesc

%==========================================================================
%\subsection {Variable-width math spaces}
\subsection {å¯å˜å®½åº¦æ•°å­¦é—´éš”}

%\begindesc
%\cts mkern {\&lt;mudimen&gt;}
%\explain
%^^{kerns//in math formulas}
%This command
%produces a \minref{kern}, i.e., blank space, of width \&lt;mudimen&gt;.
%The kern is measured
%in \minref{mathematical unit}s, which vary according to the style.
%Aside from its unit of measurement, this command behaves just like
%|\kern| (\xref \kern) does in horizontal mode.
\begindesc
\cts mkern {\&lt;mudimen&gt;}
\explain
^^{ç´§æŽ’//æ•°å­¦å…¬å¼ä¸­çš„ç´§æŽ’}
æ­¤å‘½ä»¤ç”Ÿæˆä¸€ä¸ªå®½åº¦ä¸º \&lt;mudimen&gt; çš„\minref{ç´§æŽ’}ï¼Œå³ç©ºç™½é—´éš”ã€‚
è¯¥ç´§æŽ’ç”¨\minref{æ•°å­¦å•ä½}è¡¨ç¤ºï¼Œå›&nbsp;æ­¤åœ¨ä¸åŒæ&nbsp;·å¼ä¸­æœ‰ä¸åŒçš„å°ºå¯¸ã€‚
é™¤äº†ä½¿ç”¨æ•°å­¦å•ä½å¤–ï¼Œæ­¤å‘½ä»¤ä¸Žæ°´å¹³æ¨¡å¼çš„|\kern|ï¼ˆ\xref\kern ï¼‰çš„è¡¨çŽ°ç±»ä¼¼ã€‚

%\example
%$0\mkern13mu 0 \qquad {\scriptscriptstyle 0 \mkern13mu 0}$
%|
%\produces
%$0\mkern13mu 0 \qquad {\scriptscriptstyle 0 \mkern13mu 0}$
%\endexample
%\enddesc
\example
$0\mkern13mu 0 \qquad {\scriptscriptstyle 0 \mkern13mu 0}$
|
\produces
$0\mkern13mu 0 \qquad {\scriptscriptstyle 0 \mkern13mu 0}$
\endexample
\enddesc

%\begindesc
%\cts mskip {\&lt;mudimen$_1$&gt; {\bt plus} \&lt;mudimen$_2$&gt; {\bt minus}
%   \&lt;mudimen$_3$&gt;}
%\explain
%^^{glue}
%This command produces horizontal \minref{glue}
%that has natural width \&lt;mu\-dimen$_1$&gt;, stretch \&lt;mudimen$_2$&gt;,
%and shrink \&lt;mudimen$_3$&gt;.
%The glue is measured in \minref{mathematical unit}s, which vary according
%to the style.  Aside from its units of measurement, this command behaves
%just like |\hskip| (\xref \hskip).
\begindesc
\cts mskip {\&lt;mudimen$_1$&gt; {\bt plus} \&lt;mudimen$_2$&gt; {\bt minus}
   \&lt;mudimen$_3$&gt;}
\explain
^^{ç²˜è¿ž}
æ­¤å‘½ä»¤ç”Ÿæˆä¸€ä¸ªæ°´å¹³\minref{ç²˜è¿ž}ï¼Œå®ƒçš„è‡ªç„¶å®½åº¦ä¸º \&lt;mu\-dimen$_1$&gt;ï¼Œ
ä¼¸é•¿é‡ä¸º \&lt;mudimen$_2$&gt;ï¼Œæ”¶ç¼©é‡ä¸º \&lt;mudimen$_3$&gt;ã€‚
è¯¥ç²˜è¿žç”¨\minref{æ•°å­¦å•ä½}è¡¨ç¤ºï¼Œå›&nbsp;æ­¤å°†éšç€æ&nbsp;·å¼çš„å˜åŒ–è€Œå˜åŒ–ã€‚
é™¤äº†ä½¿ç”¨æ•°å­¦å•ä½å¤–ï¼Œæ­¤å‘½ä»¤ä¸Ž |\hskip|ï¼ˆ\xref\hskip ï¼‰çš„è¡¨çŽ°ç±»ä¼¼ã€‚

%\example
%$0\mskip 13mu 0 \quad {\scriptscriptstyle 0 \mskip 13mu 0}$
%|
%\produces
%$0\mskip 13mu 0 \quad {\scriptscriptstyle 0 \mskip 13mu 0}$
%\endexample
%\enddesc
\example
$0\mskip 13mu 0 \quad {\scriptscriptstyle 0 \mskip 13mu 0}$
|
\produces
$0\mskip 13mu 0 \quad {\scriptscriptstyle 0 \mskip 13mu 0}$
\endexample
\enddesc

%\begindesc
%\cts nonscript {}
%\explain
%When \TeX\ is currently typesetting in script or scriptscript
%\minref{style} and encounters this command
%immediately in front of glue or a kern,
%it cancels the glue or kern.
%|\nonscript| has no effect in the other styles.
\begindesc
\cts nonscript {}
\explain
åœ¨æŽ’ç‰ˆæ&nbsp;‡å·æˆ–å°æ&nbsp;‡å·\minref{æ&nbsp;·å¼}æ—¶ï¼Œå¦‚æžœ \TeX\ åœ¨ç²˜è¿žæˆ–ç´§æŽ’è·Ÿå‰é‡åˆ°æ­¤å‘½ä»¤ï¼Œ
å®ƒå°±ä¸¢å¼ƒè¯¥ç²˜è¿žæˆ–ç´§æŽ’ã€‚|\nonscript| åœ¨å…¶ä»–æ&nbsp;·å¼ä¸­æ—&nbsp;ä»»ä½•æ•ˆæžœã€‚

%This command provides a way of ``tightening up'' the spacing in
%script and scriptscript styles, which generally are set in smaller type.
%It is of little use outside of macro definitions.
%\example
%\def\ab{a\nonscript\; b}
%$\ab^{\ab}$
%|
%\produces
%\def\ab{a\nonscript\; b}
%$\ab^{\ab}$
%\endexample
%\enddesc
æ­¤å‘½ä»¤æä¾›ä¸€ç§``æ”¶ç´§''æ&nbsp;‡å·å’Œå°æ&nbsp;‡å·æ&nbsp;·å¼ä¸­çš„é—´éš”çš„æ–¹æ³•ï¼›
é€šå¸¸ç”¨å°å·å­—ä½“æŽ’ç‰ˆè¿™ä¸¤ä¸ªæ&nbsp;·å¼ã€‚åœ¨å®å®šä¹‰ä¹‹å¤–çš„åœ°æ–¹ï¼Œæ­¤å‘½ä»¤å¾ˆå°‘ç”¨åˆ°ã€‚
\example
\def\ab{a\nonscript\; b}
$\ab^{\ab}$
|
\produces
\def\ab{a\nonscript\; b}
$\ab^{\ab}$
\endexample
\enddesc

%\see |\kern| (\xref\kern), |\hskip| (\xref\hskip).
%\eix^^{space//in math formulas}
\see |\kern|ï¼ˆ\xref\kern ï¼‰å’Œ |\hskip|ï¼ˆ\xref\hskip ï¼‰ã€‚
\eix^^{é—´éš”//æ•°å­¦å…¬å¼ä¸­çš„é—´éš”}

%==========================================================================
%\subsection {Spacing parameters for displays}
\subsection {é™ˆåˆ—å…¬å¼çš„é—´éš”å‚æ•°}

%\begindesc
%\bix^^{displays//spacing parameters for}
%\cts displaywidth {\param{dimen}}
%\explain
%This parameter specifies the maximum width that
%\TeX\ allows for a math display.  If \TeX\ cannot fit the display
%into a space of this width, it sets an overfull \minref{hbox}
%and complains.
%\TeX\ sets the value of |\displaywidth| when it encounters the `|$$|'
%that starts the display.  This initial value is
%|\hsize| (\xref \hsize) unless it's overridden by changes to the
%paragraph shape.
%See \knuth{pages~188--189} for a more detailed explanation of this parameter.
%\enddesc
\begindesc
\bix^^{é™ˆåˆ—å…¬å¼//é™ˆåˆ—å…¬å¼çš„é—´éš”å‚æ•°}
\cts displaywidth {\param{dimen}}
\explain
æ­¤å‚æ•°æŒ‡å®š \TeX\ å¯¹é™ˆåˆ—å…¬å¼æ‰€å…è®¸çš„æœ€å¤§å®½åº¦ã€‚
å¦‚æžœ \TeX\ æ—&nbsp;æ³•å°†é™ˆåˆ—å…¬å¼æ”¾å…¥è¿™æ&nbsp;·å®½çš„ç©ºé—´ä¸­ï¼Œ
å®ƒå°†ç”Ÿæˆä¸€ä¸ªè¿‡æ»¡çš„\minref{æ°´å¹³ç›’å­}å¹¶ç»™å‡ºè­¦å‘Šã€‚
\TeX\ åœ¨é‡åˆ° `|$$|' å¼€å§‹é™ˆåˆ—å…¬å¼æ—¶å°±è®¾å®š |\displaywidth| çš„å€¼ã€‚
å®ƒçš„åˆå§‹å€¼ä¸º |\hsize|ï¼ˆ\xref\hsize ï¼‰ï¼Œé™¤éžæ®µè½å½¢çŠ¶æ”¹å˜äº†ã€‚
è§\knuth{ç¬¬~188--189~é¡µ}ä¸­å¯¹æ­¤å‚æ•°çš„æ›´ä»”ç»†çš„è¯´æ˜Žã€‚
\enddesc

%\begindesc
%\cts displayindent {\param{dimen}}
%\explain
%This parameter specifies the space by which \TeX\ indents a
%math display.
%\TeX\ sets the value of |\displayindent| when it encounters the `|$$|'
%that starts the display.  Usually this initial value is zero,
%but if the paragraph shape indicates that the display should
%be shifted by an amount $s$,
%\TeX\ will set |\displayindent| to $s$.
%See \knuth{pages~188--189} for a more detailed explanation of this parameter.
%\enddesc
\begindesc
\cts displayindent {\param{dimen}}
\explain
æ­¤å‚æ•°æŒ‡å®š \TeX\ å¯¹é™ˆåˆ—å…¬å¼çš„ç¼©è¿›é‡ã€‚
\TeX\ åœ¨é‡åˆ° `|$$|' å¼€å§‹é™ˆåˆ—å…¬å¼æ—¶å°±è®¾å®š |\displayindent| çš„å€¼ã€‚
é€šå¸¸å®ƒçš„åˆå§‹å€¼ä¸ºé›¶ï¼Œä½†å¦‚æžœæ®µè½å½¢çŠ¶è¡¨æ˜Žè¯¥é™ˆåˆ—å…¬å¼éœ€è¦ç§»åŠ¨è·ç¦» $s$ï¼Œ
\TeX\ å°±è®¾å®š |\displayindent| ç­‰äºŽ $s$ã€‚
è§\knuth{ç¬¬~188--189~é¡µ}ä¸­å¯¹æ­¤å‚æ•°çš„æ›´ä»”ç»†çš„ä»‹ç»ã€‚
\enddesc

%\begindesc
%\cts predisplaysize {\param{dimen}}
%\explain
%\TeX\ sets this parameter to the width of the line preceding
%a math display.
%\TeX\ uses |\predisplaysize| to determine whether or not
%the display starts to
%the left of where the previous line ends, i.e., whether or not it visually
%overlaps the previous line.
%If there is overlap, it uses the |\abovedisplayskip| and
%|\belowdisplayskip| glue in setting the display;
%otherwise it uses the |\abovedisplay!-shortskip| and
%|\belowdisplay!-shortskip| glue.
%See \knuth{pages~188--189} for a more detailed explanation of this parameter.
%\enddesc
\begindesc
\cts predisplaysize {\param{dimen}}
\explain
\TeX\ è®¾å®šæ­¤å‚æ•°ç­‰äºŽé™ˆåˆ—å…¬å¼ä¹‹å‰çš„æ–‡æœ¬è¡Œçš„å®½åº¦ã€‚
\TeX\ åˆ©ç”¨ |\predisplaysize| ç¡®å®šæ˜¯å¦è®©é™ˆåˆ—å…¬å¼çš„èµ·å§‹ç‚¹ä½äºŽå‰ä¸€è¡Œç»“å°¾å¤„çš„å·¦è¾¹ï¼Œ
å³å®ƒåœ¨å¤–è§‚ä¸Šæ˜¯å¦å¯èƒ½ä¸Žå‰ä¸€è¡Œé‡å&nbsp;ã€‚å¦‚æžœä¼šæœ‰é‡å&nbsp;ï¼Œ
\TeX\ åœ¨æŽ’ç‰ˆé™ˆåˆ—å…¬å¼æ—¶ä½¿ç”¨|\abovedisplayskip| å’Œ |\belowdisplayskip| ç²˜è¿žï¼›
å¦åˆ™ \TeX\ ä½¿ç”¨ |\abovedisplay!-shortskip| å’Œ |\belowdisplay!-shortskip| ç²˜è¿žã€‚
è§\knuth{ç¬¬~188--189~é¡µ}ä¸­å¯¹æ­¤å‚æ•°çš„æ›´ä»”ç»†çš„ä»‹ç»ã€‚
\enddesc

%\begindesc
%\cts abovedisplayskip {\param{glue}}
%\explain
%This parameter specifies the amount of vertical glue that
%\TeX\ inserts before a display when the display starts to
%the left of where the previous line ends, i.e., when it visually
%overlaps the previous line.
%\PlainTeX\ sets |\abovedisplayskip| to |12pt plus3pt minus9pt|.
%See \knuth{pages~188--189} for a more detailed explanation of this parameter.
%\enddesc
\begindesc
\cts abovedisplayskip {\param{glue}}
\explain
æ­¤å‘½ä»¤æŒ‡å®šå½“é™ˆåˆ—å…¬å¼çš„èµ·å§‹ç‚¹ä½äºŽå‰ä¸€è¡Œç»“å°¾å¤„çš„å·¦è¾¹æ—¶ï¼Œ
å³å®ƒåœ¨å¤–è§‚ä¸Šå¯èƒ½ä¸Žå‰ä¸€è¡Œæœ‰é‡å&nbsp;æ—¶ï¼Œ
\TeX\ åœ¨é™ˆåˆ—å…¬å¼ä¹‹å‰æ’å…¥çš„ç«–ç›´ç²˜è¿žçš„å¤§å°ã€‚
\PlainTeX\ è®¾å®š |\abovedisplayskip| ç­‰äºŽ |12pt plus3pt minus9pt|ã€‚
è§\knuth{ç¬¬~188--189~é¡µ}ä¸­å¯¹æ­¤å‚æ•°çš„æ›´ä»”ç»†çš„ä»‹ç»ã€‚
\enddesc

%\begindesc
%\cts belowdisplayskip {\param{glue}}
%\explain
%This parameter specifies the amount of vertical glue that
%\TeX\ inserts after a display when the display starts to
%the left of where the previous line ends, i.e., when it visually
%overlaps the previous line.
%\PlainTeX\ sets |\belowdisplay!-skip| to |12pt plus3pt minus9pt|.
%See \knuth{pages~188--189} for a more detailed explanation of this parameter.
%\enddesc
\begindesc
\cts belowdisplayskip {\param{glue}}
\explain
æ­¤å‘½ä»¤æŒ‡å®šå½“é™ˆåˆ—å…¬å¼çš„èµ·å§‹ç‚¹ä½äºŽå‰ä¸€è¡Œç»“å°¾å¤„çš„å·¦è¾¹æ—¶ï¼Œ
å³å®ƒåœ¨å¤–è§‚ä¸Šå¯èƒ½ä¸Žå‰ä¸€è¡Œæœ‰é‡å&nbsp;æ—¶ï¼Œ
\TeX\ åœ¨é™ˆåˆ—å…¬å¼ä¹‹åŽæ’å…¥çš„ç«–ç›´ç²˜è¿žçš„å¤§å°ã€‚
\PlainTeX\ è®¾å®š |\belowdisplay!-skip| ç­‰äºŽ |12pt plus3pt minus9pt|ã€‚
è§\knuth{ç¬¬~188--189~é¡µ}ä¸­å¯¹æ­¤å‚æ•°çš„æ›´ä»”ç»†çš„ä»‹ç»ã€‚
\enddesc

%\begindesc
%\cts abovedisplayshortskip {\param{glue}}
%\explain
%This parameter specifies the amount of vertical glue that
%\TeX\ inserts before a math display
%when the display starts to
%the right of where the previous line ends, i.e., when it does not visually
%overlap the previous line.
%\PlainTeX\ sets |\abovedisplay!-shortskip| to |0pt plus3pt|.
%See \knuth{pages~188--189} for a more detailed explanation of this parameter.
%\enddesc
\begindesc
\cts abovedisplayshortskip {\param{glue}}
\explain
æ­¤å‘½ä»¤æŒ‡å®šå½“é™ˆåˆ—å…¬å¼çš„èµ·å§‹ç‚¹ä½äºŽå‰ä¸€è¡Œç»“å°¾å¤„çš„å³è¾¹æ—¶ï¼Œ
å³å®ƒåœ¨å¤–è§‚ä¸Šä¸ä¼šä¸Žå‰ä¸€è¡Œæœ‰é‡å&nbsp;æ—¶ï¼Œ
\TeX\ åœ¨é™ˆåˆ—å…¬å¼ä¹‹å‰æ’å…¥çš„ç«–ç›´ç²˜è¿žçš„å¤§å°ã€‚
\PlainTeX\ è®¾å®š |\abovedisplay!-shortskip| ç­‰äºŽ |0pt plus3pt|ã€‚
è§\knuth{ç¬¬~188--189~é¡µ}ä¸­å¯¹æ­¤å‚æ•°çš„æ›´ä»”ç»†çš„ä»‹ç»ã€‚
\enddesc

%\begindesc
%\cts belowdisplayshortskip {\param{glue}}
%\explain
%This parameter specifies the amount of vertical glue that
%\TeX\ inserts after a display
%when the display starts to
%the right of where the previous line ends, i.e., when it does not visually
%overlap the previous line.
%\PlainTeX\ sets |\belowdisplay!-shortskip| to |7pt plus3pt minus4pt|.
%See \knuth{pages~188--189} for a more detailed explanation of this parameter.
\begindesc
\cts belowdisplayshortskip {\param{glue}}
\explain
æ­¤å‘½ä»¤æŒ‡å®šå½“é™ˆåˆ—å…¬å¼çš„èµ·å§‹ç‚¹ä½äºŽå‰ä¸€è¡Œç»“å°¾å¤„çš„å³è¾¹æ—¶ï¼Œ
å³å®ƒåœ¨å¤–è§‚ä¸Šä¸ä¼šä¸Žå‰ä¸€è¡Œæœ‰é‡å&nbsp;æ—¶ï¼Œ
\TeX\ åœ¨é™ˆåˆ—å…¬å¼ä¹‹åŽæ’å…¥çš„ç«–ç›´ç²˜è¿žçš„å¤§å°ã€‚
\PlainTeX\ è®¾å®š |\belowdisplay!-shortskip| ç­‰äºŽ |7pt plus3pt minus4pt|ã€‚
è§\knuth{ç¬¬~188--189~é¡µ}ä¸­å¯¹æ­¤å‚æ•°çš„æ›´ä»”ç»†çš„ä»‹ç»ã€‚

%\eix^^{displays//spacing parameters for}
%\enddesc
\eix^^{é™ˆåˆ—å…¬å¼//é™ˆåˆ—å…¬å¼çš„é—´éš”å‚æ•°}
\enddesc


%==========================================================================
\subsection {å…¶ä»–çš„æ•°å­¦é—´éš”å‚æ•°}

%\begindesc
%\cts mathsurround {\param{dimen}}
%\explain
%This parameter specifies the amount of space that \TeX\
%inserts before and after a math formula in text mode (i.e., a formula
%surrounded by single |$|'s).  See \knuth{page~162} for further details about
%its behavior.
%\PlainTeX\ leaves |\mathsurround| at |0pt|.
%\enddesc
\begindesc
\cts mathsurround {\param{dimen}}
\explain
æ­¤å‚æ•°æŒ‡å®š \TeX\ åœ¨æ–‡å†…æ•°å­¦å…¬å¼ï¼ˆå³æ”¾åœ¨ä¸¤ä¸ª|$|ä¹‹é—´çš„å…¬å¼ï¼‰ä¸¤è¾¹æ’å…¥çš„é—´éš”çš„å¤§å°ã€‚
è§\knuth{ç¬¬~162~é¡µ}å¯¹æ­¤è¡Œä¸ºçš„è¿›ä¸€æ­¥è§£é‡Šã€‚
\PlainTeX\ è®¾å®š |\mathsurround| ä¸º |0pt|ã€‚
\enddesc

%\begindesc
%\cts nulldelimiterspace {\param{dimen}}
%\explain
%^^{delimiters//null, space for}
%This parameter specifies the width of the
%space produced by a null \minref{delimiter}.
%\PlainTeX\ sets |\nulldelimiterspace| to |1.2pt|.
%\enddesc
\begindesc
\cts nulldelimiterspace {\param{dimen}}
\explain
^^{å®šç•Œç¬¦//ç©ºå®šç•Œç¬¦çš„é—´éš”}
æ­¤å‚æ•°æŒ‡å®šç©º\minref{å®šç•Œç¬¦}ç”Ÿæˆçš„é—´éš”çš„å¤§å°ã€‚
\PlainTeX\ è®¾å®š |\null!-delimiterspace| ç­‰äºŽ |1.2pt|ã€‚
\enddesc

%\begindesc
%\cts scriptspace {\param{dimen}}
%\explain
%This parameter specifies the amount of space that \TeX\
%inserts before and after a subscript or superscript.
%The |\nonscript| command (\xref\nonscript) ^^|\nonscript|
%after a subscript or superscript cancels this space.
%\PlainTeX\ sets |\script!-space| to |0.5pt|.
%\enddesc
\begindesc
\cts scriptspace {\param{dimen}}
\explain
æ­¤å‚æ•°æŒ‡å®š \TeX\ åœ¨ä¸Šæ&nbsp;‡æˆ–ä¸‹æ&nbsp;‡å‰åŽæ’å…¥çš„é—´éš”çš„å¤§å°ã€‚
ä¸Šæ&nbsp;‡æˆ–ä¸‹æ&nbsp;‡ä¹‹åŽçš„ |\nonscript| å‘½ä»¤ï¼ˆ\xref\nonscript ï¼‰^^|\nonscript|
å¯ä»¥å–æ¶ˆæ­¤é—´éš”ã€‚
\PlainTeX\ è®¾å®š |\script!-space| ç­‰äºŽ |0.5pt|ã€‚
\enddesc


%==========================================================================
%\section {Categorizing math constructs}
\section {åˆ†ç±»æ•°å­¦ç»“æž„}

%\begindesc
%\makecolumns 7/2:
%\cts mathord {}
%\cts mathop {}
%\cts mathbin {}
%\cts mathrel {}
%\cts mathopen {}
%\cts mathclose {}
%\cts mathpunct {}
%\explain
%These commands tell \TeX\ to treat the construct that follows as belonging
%to a particular ^{class} (see \knuth{page~154} for the definition
%of the classes).  They are listed here in the order of the class numbers,
%from $0$ to $6$.  Their primary
%effect is to adjust the spacing around the construct
%to be whatever it is for the specified class.
\begindesc
\makecolumns 7/2:
\cts mathord {}
\cts mathop {}
\cts mathbin {}
\cts mathrel {}
\cts mathopen {}
\cts mathclose {}
\cts mathpunct {}
\explain
è¿™äº›å‘½ä»¤è®© \TeX\ æŠŠéšåŽçš„ç»“æž„å½’å…¥æŒ‡å®šçš„^{ç±»}ï¼ˆè§\knuth{ç¬¬~154~é¡µ}å¯¹ç±»çš„å®šä¹‰ï¼‰ã€‚
å®ƒä»¬æŒ‰ç…§ç±»ç¼–å·çš„å¤§å°é¡ºåºæŽ’åˆ—ï¼Œä»Ž $0$ åˆ° $6$ã€‚
å®ƒä»¬ä¸»è¦ç”¨äºŽæŒ‰ç…§æŒ‡å®šçš„ç±»è°ƒæ•´è¯¥ç»“æž„ä¸¤è¾¹çš„é—´éš”å¤§å°ã€‚
%\example
%$\mathop{\rm minmax}\limits_{t \in A \cup B}\,t$
%% By treating minmax as a math operator, we can get TeX to
%% put something underneath it.
%|
%\produces
%$\mathop{\rm minmax}\limits_{t \in A \cup B}\,t$
%\endexample
%\enddesc
\example
$\mathop{\rm minmax}\limits_{t \in A \cup B}\,t$
% By treating minmax as a math operator, we can get TeX to
% put something underneath it.
|
\produces
$\mathop{\rm minmax}\limits_{t \in A \cup B}\,t$
\endexample
\enddesc

%\begindesc
%\cts mathinner {}
%\explain
%This command tells \TeX\ to treat the construct that follows
%as an ``inner formula'', e.g., a fraction, for spacing purposes.
%It resembles the class commands given just above.
%\enddesc
\begindesc
\cts mathinner {}
\explain
æ­¤å‘½ä»¤è®© \TeX\ å°†éšåŽçš„ç»“æž„è§†ä¸º``å†…éƒ¨å…¬å¼''ï¼Œæ¯”å¦‚åˆ†å¼ï¼Œå¹¶æ®æ­¤è°ƒæ•´é—´éš”ã€‚
å®ƒä¸Žä¸Šé¢åˆšæåˆ°çš„ç±»å‘½ä»¤ç±»ä¼¼ã€‚
\enddesc

%==========================================================================
%\section {Special actions for math formulas}
\section {ç‰¹æ®Šå¤„ç†æ•°å­¦å…¬å¼}

%\begindesc
%\cts everymath {\param{token list}}
%\cts everydisplay {\param{token list}}
%\explain
%^^{displays//actions for every display}
%These parameters specify \minref{token} lists that \TeX\ inserts
%at the start of every text math or display math formula, respectively.
%You can
%take special actions at the start of each math formula by
%assigning those actions to |\everymath| or
%|\everydisplay|.  Don't forget that if you want both kinds of formulas to
%be affected, you need to set \emph{both} parameters.
%\example
%\everydisplay={\heartsuit\quad}
%\everymath = {\clubsuit}
%$3$ is greater than $2$ for large values of $3$.
%$$4&gt;3$$
%|
%\produces
%\everydisplay={\heartsuit\quad}
%\everymath = {\clubsuit}
%$3$ is greater than $2$ for large values of $3$.
%$$4&gt;3$$
%\endexample
%\enddesc
\begindesc
\cts everymath {\param{token list}}
\cts everydisplay {\param{token list}}
\explain
^^{é™ˆåˆ—å…¬å¼//ä½œç”¨åˆ°æ¯ä¸ªé™ˆåˆ—å…¬å¼}
è¿™ä¸¤ä¸ªå‘½ä»¤åˆ†åˆ«æŒ‡å®š \TeX\ åœ¨æ¯ä¸ªæ–‡å†…å…¬å¼æˆ–é™ˆåˆ—å…¬å¼å¼€å¤´æ’å…¥çš„\minref{è®°å·}åˆ—ã€‚
ä½&nbsp;å¯ä»¥åˆ©ç”¨ |\everymath| æˆ– |\everydisplay| åœ¨æ¯ä¸ªæ•°å­¦å…¬å¼å¼€å¤´ä½œç‰¹æ®Šå¤„ç†ã€‚
ä½&nbsp;åŠ¡å¿…æ¸…æ¥šï¼Œè‹¥ä½&nbsp;éœ€è¦åŒæ—¶å¤„ç†ä¸¤ç§å…¬å¼ï¼Œä½&nbsp;å¿…é¡»\emph{åŒæ—¶}è®¾å®šè¿™ä¸¤ä¸ªå‚æ•°ã€‚
\example
\everydisplay={\heartsuit\quad}
\everymath = {\clubsuit}
$3$ is greater than $2$ for large values of $3$.
$$4&gt;3$$
|
\produces
\everydisplay={\heartsuit\quad}
\everymath = {\clubsuit}
$3$ is greater than $2$ for large values of $3$.
$$4&gt;3$$
\endexample
\enddesc

%\enddescriptions
%\eix^^{math}
%\endchapter
%\byebye
\enddescriptions
\eix^^{æ•°å­¦}

\ifoldeplain\else\ifcompletebook\else
\vskip4em{\sectionfonts\leftline{æœ¬ç«&nbsp;ç´¢å¼•}}
\readindexfile{i}
\fi\fi

\endchapter
\byebye
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